A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.

Polytope elements

Polygon (2-polytope)

* Vertex the ''ridge'' or ''(n−2)-face'' of the polygon * Edge the ''facet'' or ''(n−1)-face'' of the polygon

Polyhedron (3-polytope)

* Vertex the ''peak'' or ''(n−3)-face'' of the polyhedron * Edge the ''ridge'' or ''(n−2)-face'' of the polyhedron *

Face The face is the front of the head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affect th ...

the ''facet'' or ''(n−1)-face'' of the polyhedron

Polychoron (4-polytope)

* Vertex the ''(n−4)-face'' of the polychoron * Edge the ''peak'' or ''(n−3)-face'' of the polychoron *

the ''ridge'' or ''(n−2)-face'' of the polychoron * Cell the ''facet'' or ''(n−1)-face'' of the polychoron

5-polytope

* Vertex the ''(n−5)-face'' of the 5-polytope * Edge the ''(n−4)-face'' of the 5-polytope *

the ''peak'' or ''(n−3)-face'' of the 5-polytope * Cell the ''ridge'' or ''(n−2)-face'' of the 5-polytope * Hypercell or Teron the ''facet'' or ''(n−1)-face'' of the 5-polytope

Other

* Point *

Line segment In geometry, a line segment is a part of a line (mathematics), straight line that is bounded by two distinct endpoints (its extreme points), and contains every Point (geometry), point on the line that is between its endpoints. It is a special c ...

Vertex figure In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a general -polytope is sliced off. Definitions Take some corner or Vertex (geometry), vertex of a polyhedron. Mark a point somewhere along each connected ed ...

* Peak – ''(n−3)-face'' *

Ridge A ridge is a long, narrow, elevated geomorphologic landform, structural feature, or a combination of both separated from the surrounding terrain by steep sides. The sides of a ridge slope away from a narrow top, the crest or ridgecrest, wi ...

– ''(n−2)-face'' *

Facet Facets () are flat faces on geometric shapes. The organization of naturally occurring facets was key to early developments in crystallography, since they reflect the underlying symmetry of the crystal structure. Gemstones commonly have facets cu ...

– ''(n−1)-face''

Two dimensional (
polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...
s)

Triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...

Equilateral triangle An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the ...

Isosceles triangle In geometry, an isosceles triangle () is a triangle that has two Edge (geometry), sides of equal length and two angles of equal measure. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at le ...

*** Golden triangle (mathematics) **

Scalene triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional ...

Right triangle A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle ( turn or 90 degrees). The side opposite to the right angle i ...

** Oblique triangle ***

Acute triangle An acute triangle (or acute-angled triangle) is a triangle with three ''acute angles'' (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle with one ''obtuse angle'' (greater than 90°) and two acute angles. Since a triang ...

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Obtuse Triangle An acute triangle (or acute-angled triangle) is a triangle with three ''acute angles'' (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle with one '' obtuse angle'' (greater than 90°) and two acute angles. Since a trian ...

Quadrilateral In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''l ...

Rectangle In Euclidean geometry, Euclidean plane geometry, a rectangle is a Rectilinear polygon, rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that a ...

***

Square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

****

Unit square In mathematics, a unit square is a square whose sides have length . Often, ''the'' unit square refers specifically to the square in the Cartesian plane with corners at the four points ), , , and . Cartesian coordinates In a Cartesian coordinat ...

***

Oblong An oblong is an object longer than it is wide, especially a non-square rectangle. Oblong may also refer to: Places * Oblong, Illinois, a village in the United States * Oblong Township, Crawford County, Illinois, United States * A strip of land ...

**** Golden rectangle **** Silver rectangle **** Ailles rectangle **

Rhombus In plane Euclidean geometry, a rhombus (: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhom ...

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Golden Rhombus In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio: : = \varphi = \approx 1.618~034 Equivalently, it is the Varignon parallelogram formed from the edge midpoints of a golden rectangle. Rhombi with this shape f ...

Parallelogram In Euclidean geometry, a parallelogram is a simple polygon, simple (non-list of self-intersecting polygons, self-intersecting) quadrilateral with two pairs of Parallel (geometry), parallel sides. The opposite or facing sides of a parallelogram a ...

***

Rhomboid Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled. The terms "rhomboid" and "parallelogram" are often erroneously conflated with each oth ...

Trapezoid In geometry, a trapezoid () in North American English, or trapezium () in British English, is a quadrilateral that has at least one pair of parallel sides. The parallel sides are called the ''bases'' of the trapezoid. The other two sides are ...

***

Isosceles trapezoid In Euclidean geometry, an isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and bo ...

Kite A kite is a tethered heavier than air flight, heavier-than-air craft with wing surfaces that react against the air to create Lift (force), lift and Drag (physics), drag forces. A kite consists of wings, tethers and anchors. Kites often have ...

*** Lute of pythagoras *** Right Kite **

Antiparallelogram In geometry, an antiparallelogram is a type of list of self-intersecting polygons, self-crossing quadrilateral. Like a parallelogram, an antiparallelogram has two opposite pairs of equal-length sides, but these pairs of sides are not in general ...

Pentagon In geometry, a pentagon () is any five-sided polygon or 5-gon. The sum of the internal angles in a simple polygon, simple pentagon is 540°. A pentagon may be simple or list of self-intersecting polygons, self-intersecting. A self-intersecting ...

Hexagon In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is de ...

* Heptagon *

Octagon In geometry, an octagon () is an eight-sided polygon or 8-gon. A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, which alternates two types of edges. A truncated octagon, t is a ...

Nonagon In geometry, a nonagon () or enneagon () is a nine-sided polygon or 9-gon. The name ''nonagon'' is a prefix Hybrid word, hybrid formation, from Latin (''nonus'', "ninth" + ''gonon''), used equivalently, attested already in the 16th century in Fre ...

* Decagon * Hendecagon *

Dodecagon In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon. Regular dodecagon A regular polygon, regular dodecagon is a figure with sides of the same length and internal angles of the same size. It has twelve lines of reflective symmetry ...

* Triskaidecagon * Tetradecagon *

Pentadecagon In geometry, a pentadecagon or pentakaidecagon or 15-gon is a fifteen-sided polygon. Regular pentadecagon A '' regular pentadecagon'' is represented by Schläfli symbol . A regular pentadecagon has interior angles of 156 °, and with a side ...

Hexadecagon In mathematics, a hexadecagon (sometimes called a hexakaidecagon or 16-gon) is a sixteen-sided polygon. Regular hexadecagon A ''regular polygon, regular hexadecagon'' is a hexadecagon in which all angles are equal and all sides are congruent. It ...

* Heptadecagon *

Octadecagon In geometry, an octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon. Regular octadecagon A ''regular polygon, regular octadecagon'' has a Schläfli symbol and can be constructed as a quasiregular Truncation (geometry), trunc ...

* Enneadecagon *

Icosagon In geometry, an icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees. Regular icosagon The Regular polygon, regular icosagon has Schläfli symbol , and can also be constructed as a Truncation ( ...

* Icosihenagon * Icosidigon * Icositrigon *

Icositetragon In geometry, an icositetragon (or icosikaitetragon) or 24-gon is a twenty-four-sided polygon. The sum of any icositetragon's interior angles is 3960 degrees. Regular icositetragon The ''regular polygon, regular icositetragon'' is represented by S ...

* Icosipentagon * Icosihexagon * Icosiheptagon * Icosioctagon * Icosienneagon * Triacontagon * Tetracontagon * Pentacontagon * Hexacontagon * Heptacontagon * Octacontagon * Enneacontagon * Hectogon *

257-gon In geometry, a 257-gon is a polygon with 257 sides. The sum of the interior angles of any non- self-intersecting 257-gon is 45,900°. Regular 257-gon The area of a regular 257-gon is (with ) :A = \frac t^2 \cot \frac\approx 5255.751t^2. A wh ...

* Chiliagon * Myriagon * 65537-gon * Megagon * Gigagon * Teragon * Apeirogon

Star polygon In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, Decagram (geometry)#Related figures, certain notable ones can ...
s

Pentagram A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle around ...

Hexagram , can be seen as a compound polygon, compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green). A hexagram (Greek language, Greek) or sexagram (Latin l ...

* Heptagram *

Octagram In geometry, an octagram is an eight-angled star polygon. The name ''octagram'' combine a Greek numeral prefix, ''wikt:octa-, octa-'', with the Greek language, Greek suffix ''wikt:-gram, -gram''. The ''-gram'' suffix derives from γραμμή ...

* Enneagram * Decagram * Hendecagram *

Dodecagram In geometry, a dodecagram (γραμμή
Henry George Liddell, Robe ...

Icositetragram In geometry, an icositetragon (or icosikaitetragon) or 24-gon is a twenty-four-sided polygon. The sum of any icositetragon's interior angles is 3960 degrees. Regular icositetragon The ''regular polygon, regular icositetragon'' is represented by S ...

Families

Concave polygon A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that is, an angle with a measure that is between 180° degrees and 360° degrees exclusive. ...

Cyclic polygon In geometry, a set (mathematics), set of point (geometry), points are said to be concyclic (or cocyclic) if they lie on a common circle. A polygon whose vertex (geometry), vertices are concyclic is called a cyclic polygon, and the circle is cal ...

Regular polygon In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either ''convex ...

Polyform In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a trian ...

* Gnomon * Golygon

Tilings

List of uniform tilings Uniform tilings in hyperbolic plane ; Archimedean tiling *

Square tiling In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane consisting of four squares around every vertex. John Horton Conway called it a quadrille. Structure and properties The square tili ...

* Triangular tiling *

Hexagonal tiling In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of or (as a Truncation (geometry), truncated triangular tiling ...

* Truncated square tiling * Snub square tiling * Trihexagonal tiling * Truncated hexagonal tiling * Rhombitrihexagonal tiling * Truncated trihexagonal tiling * Snub hexagonal tiling * Elongated triangular tiling

Three dimensional (
polyhedra In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary su ...
)

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Three-dimensional space In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values ('' coordinates'') are required to determine the position of a point. Most commonly, it is the three- ...

Regular

Regular polyhedron A regular polyhedron is a polyhedron whose symmetry group acts transitive group action, transitively on its Flag (geometry), flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In ...

Platonic solid In geometry, a Platonic solid is a Convex polytope, convex, regular polyhedron in three-dimensional space, three-dimensional Euclidean space. Being a regular polyhedron means that the face (geometry), faces are congruence (geometry), congruent (id ...

: **

Tetrahedron In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tet ...

Cube A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...

Octahedron In geometry, an octahedron (: octahedra or octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. Many types of i ...

Dodecahedron In geometry, a dodecahedron (; ) or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three Kepler–Po ...

Icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrical tha ...

*Regular spherical polyhedron ** Dihedron, Hosohedron * Kepler–Poinsot polyhedron (Regular star polyhedra) **

Small stellated dodecahedron In geometry, the small stellated dodecahedron is a Kepler–Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol . It is one of four nonconvex List of regular polytopes#Non-convex 2, regular polyhedra. It is composed of 12 pentag ...

, Great stellated dodecahedron, Great icosahedron, Great dodecahedron *Abstract regular polyhedra ( Projective polyhedron) ** Hemicube (geometry),

hemi-octahedron In geometry, a hemi-octahedron is an abstract polytope, abstract regular polyhedron, containing half the faces of a regular octahedron. It has 4 triangular faces, 6 edges, and 3 vertices. Its dual polyhedron is the Hemicube (geometry), hemicube ...

hemi-dodecahedron In geometry, a hemi-dodecahedron is an abstract polytope, abstract, regular polyhedron, containing half the Face (geometry), faces of a regular dodecahedron. It can be realized as a projective polyhedron (a tessellation of the real projective pla ...

hemi-icosahedron In geometry, a hemi-icosahedron is an abstract polytope, abstract regular polyhedron, containing half the faces of a regular icosahedron. It can be realized as a projective polyhedron (a tessellation of the real projective plane by 10 triangles), ...

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Disphenoid In geometry, a disphenoid () is a tetrahedron whose four faces are congruent acute-angled triangles. It can also be described as a tetrahedron in which every two edges that are opposite each other have equal lengths. Other names for the same ...

; Pentahedron *

Square pyramid In geometry, a square pyramid is a Pyramid (geometry), pyramid with a square base and four triangles, having a total of five faces. If the Apex (geometry), apex of the pyramid is directly above the center of the square, it is a ''right square p ...

Triangular prism In geometry, a triangular prism or trigonal prism is a Prism (geometry), prism with 2 triangular bases. If the edges pair with each triangle's vertex and if they are perpendicular to the base, it is a ''right triangular prism''. A right triangul ...

;

Hexahedron A hexahedron (: hexahedra or hexahedrons) or sexahedron (: sexahedra or sexahedrons) is any polyhedron with six faces. A cube, for example, is a regular hexahedron with all its faces square, and three squares around each vertex. There are seven ...

Parallelepiped In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term ''rhomboid'' is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. Three equiva ...

Cuboid In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six Face (geometry), faces; it has eight Vertex (geometry), vertices and twelve Edge (geometry), edges. A ''rectangular cuboid'' (sometimes also calle ...

Rhombohedron In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a special case of a parallelepiped in which all six faces are congruent rhombi. It can be used to define the rhombohedral lattice system, a honeycomb w ...

Trigonal trapezohedron In geometry, a trigonal trapezohedron is a polyhedron with six congruent quadrilateral faces, which may be scalene or rhomboid. The variety with rhombus-shaped faces faces is a rhombohedron. An alternative name for the same shape is the ''trig ...

, Pentagonal pyramid, Triangular bipyramid, quadrilateral frustum ; Heptahedron * hexagonal pyramid, pentagonal prism, tetrahemihexahedron ;

* Hexagonal prism,

Truncated tetrahedron In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 equilateral triangle faces, 12 vertices and 18 edges (of two types). It can be constructed by truncation (geometry), truncating all 4 vertices of ...

, Tetragonal trapezohedron ; Enneahedron * Octagonal pyramid, Heptagonal prism ; Decahedron * Octagonal prism, Square antiprism, Square cupola,

Pentagonal bipyramid The pentagonal bipyramid (or pentagonal dipyramid) is a polyhedron with ten triangular faces. It is constructed by attaching two pentagonal pyramids to each of their bases. If the triangular faces are equilateral, the pentagonal bipyramid is an ...

Augmented pentagonal prism Augment or augmentation may refer to: Language *Augment (Indo-European), a syllable added to the beginning of the word in certain Indo-European languages * Augment (Bantu languages), a morpheme that is prefixed to the noun class prefix of nouns ...

;

* Pentagonal antiprism, Decagonal prism, Pentagonal cupola,

Snub disphenoid In geometry, the snub disphenoid is a convex polyhedron with 12 equilateral triangles as its face (geometry), faces. It is an example of deltahedron and Johnson solid. It can be constructed in different approaches. This shape is also called Siame ...

, Elongated square bipyramid, Metabidiminished icosahedron,

Hexagonal bipyramid A hexagonal bipyramid is a polyhedron formed from two hexagonal pyramids joined at their bases. The resulting solid has 12 triangular faces, 8 vertices and 18 edges. The 12 faces are identical isosceles triangles. Although it is face-transiti ...

, Hexagonal trapezohedron,

Triakis tetrahedron In geometry, a triakis tetrahedron (or tristetrahedron, or kistetrahedron) is a solid constructed by attaching four triangular pyramids onto the triangular faces of a regular tetrahedron, a Kleetope of a tetrahedron. This replaces the equilateral ...

Rhombic dodecahedron In geometry, the rhombic dodecahedron is a Polyhedron#Convex_polyhedra, convex polyhedron with 12 congruence (geometry), congruent rhombus, rhombic face (geometry), faces. It has 24 edge (geometry), edges, and 14 vertex (geometry), vertices of 2 ...

, Hendecagonal pyramid, Trapezo-rhombic dodecahedron, Rhombo-hexagonal dodecahedron

Archimedean solids

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Archimedean solid The Archimedean solids are a set of thirteen convex polyhedra whose faces are regular polygon and are vertex-transitive, although they aren't face-transitive. The solids were named after Archimedes, although he did not claim credit for them. They ...

, Cuboctahedron, Truncated cube,

Truncated octahedron In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14 faces (8 regular hexagon, hexagons and 6 Squa ...

, Rhombicuboctahedron, Truncated cuboctahedron, Snub cube,

Icosidodecahedron In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (''icosi-'') triangular faces and twelve (''dodeca-'') pentagonal faces. An icosidodecahedron has 30 identical Vertex (geometry), vertices, with two triang ...

, Truncated dodecahedron, Truncated icosahedron, Rhombicosidodecahedron, Truncated icosidodecahedron,

Snub dodecahedron In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex Isogonal figure, isogonal nonprismatic solids constructed by two or more types of regular polygon Face (geometry), faces. The snub dod ...

Prisms and antiprisms

; Prism *

, Pentagonal prism, Hexagonal prism, Heptagonal prism, Octagonal prism, Enneagonal prism, Decagonal prism, Hendecagonal prism, Dodecagonal prism ;

Antiprism In geometry, an antiprism or is a polyhedron composed of two Parallel (geometry), parallel Euclidean group, direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway po ...

* Square antiprism, Pentagonal antiprism, Hexagonal antiprism, Heptagonal antiprism,

Octagonal antiprism In geometry, an antiprism or is a polyhedron composed of two Parallel (geometry), parallel Euclidean group, direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway po ...

, Enneagonal antiprism, Decagonal antiprism, Dodecagonal antiprism

Catalan solids

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Catalan solid The Catalan solids are the dual polyhedron, dual polyhedra of Archimedean solids. The Archimedean solids are thirteen highly-symmetric polyhedra with regular faces and symmetric vertices. The faces of the Catalan solids correspond by duality to ...

Triakis octahedron In geometry, a triakis octahedron (or trigonal trisoctahedron or kisoctahedronConway, Symmetries of things, p. 284) is an Archimedean solid, Archimedean dual solid, or a Catalan solid. Its dual is the truncated cube. It can be seen as an octahedr ...

, Tetrakis hexahedron, Deltoidal icositetrahedron, Disdyakis dodecahedron, Pentagonal icositetrahedron,

Rhombic triacontahedron The rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombus, rhombic face (geometry), faces. It has 60 edge (geometry), edges and 32 vertex ...

, Triakis icosahedron, Pentakis dodecahedron, Deltoidal hexecontahedron, Disdyakis triacontahedron, Pentagonal hexecontahedron

Bipyramids and Trapezohedron

Bipyramid In geometry, a bipyramid, dipyramid, or double pyramid is a polyhedron formed by fusing two Pyramid (geometry), pyramids together base (geometry), base-to-base. The polygonal base of each pyramid must therefore be the same, and unless otherwise ...

** Triangular bipyramid,

, Heptagonal bipyramid, Octagonal bipyramid, Decagonal bipyramid * Trapezohedron

Uniform star polyhedra

Small rhombihexahedron In geometry, the small rhombihexahedron (or small rhombicube) is a nonconvex uniform polyhedron, indexed as U18. It has 18 faces (12 squares and 6 octagons), 48 edges, and 24 vertices. Its vertex figure is an antiparallelogram. Related polyhedra ...

* Small snub icosicosidodecahedron * Small stellated truncated dodecahedron * Snub dodecadodecahedron * Snub icosidodecadodecahedron * Stellated truncated hexahedron * Tetrahemihexahedron * Truncated dodecadodecahedron * Truncated great dodecahedron * Truncated great icosahedron

Uniform prismatic star polyhedra

; Prismatic uniform polyhedron * Pentagrammic prism, Pentagrammic antiprism, Pentagrammic crossed-antiprism * Heptagrammic antiprism (7/2), Heptagrammic antiprism (7/3) * Enneagrammic antiprism (9/2). Enneagrammic antiprism (9/4) * Enneagrammic crossed-antiprism, Enneagrammic prism (9/2), Enneagrammic prism (9/4) * Decagrammic prism, Decagrammic antiprism

Johnson solids

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Johnson solid In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two Solid geometry, s ...

# Augmented dodecahedron # Augmented hexagonal prism #

Gyroelongated pentagonal pyramid In geometry, the gyroelongated pentagonal pyramid is a polyhedron constructed by attaching a pentagonal antiprism to the base of a pentagonal pyramid. An alternative name is diminished icosahedron because it can be constructed by removing a pe ...

# Gyroelongated pentagonal rotunda # Gyroelongated square bicupola # Gyroelongated square bipyramid # Gyroelongated square cupola # Gyroelongated square pyramid # Gyroelongated triangular bicupola # Gyroelongated triangular cupola # Hebesphenomegacorona # Metabiaugmented dodecahedron # Metabiaugmented hexagonal prism # Metabiaugmented truncated dodecahedron # Metabidiminished icosahedron # Metabidiminished rhombicosidodecahedron # Metabigyrate rhombicosidodecahedron # Metagyrate diminished rhombicosidodecahedron # Parabiaugmented dodecahedron # Parabiaugmented hexagonal prism # Parabiaugmented truncated dodecahedron # Parabidiminished rhombicosidodecahedron # Parabigyrate rhombicosidodecahedron # Paragyrate diminished rhombicosidodecahedron #

# Pentagonal cupola # Pentagonal gyrobicupola # Pentagonal gyrocupolarotunda # Pentagonal orthobicupola # Pentagonal orthobirotunda # Pentagonal orthocupolarotunda # Pentagonal pyramid # Pentagonal rotunda #

# Snub square antiprism # Sphenocorona # Sphenomegacorona # Square cupola # Square gyrobicupola # Square orthobicupola #

# Triangular bipyramid #

Triangular cupola In geometry, the triangular cupola is the cupola with hexagon as its base and triangle as its top. If the edges are equal in length, the triangular cupola is the Johnson solid. It can be seen as half a cuboctahedron. The triangular cupola can b ...

# Triangular hebesphenorotunda #

Triangular orthobicupola In geometry, the triangular orthobicupola is one of the Johnson solids (). As the name suggests, it can be constructed by attaching two triangular cupolas () along their bases. It has an equal number of squares and triangles at each vertex; howe ...

# Triaugmented dodecahedron # Triaugmented hexagonal prism # Triaugmented triangular prism # Triaugmented truncated dodecahedron # Tridiminished icosahedron # Tridiminished rhombicosidodecahedron # Trigyrate rhombicosidodecahedron

Dual uniform star polyhedra

Great triambic icosahedron In geometry, the great triambic icosahedron and medial triambic icosahedron (or midly triambic icosahedron) are visually identical Dual polyhedron, dual uniform polyhedra. The exterior surface also represents the The Fifty-Nine Icosahedra, De2f2 ...

* Medial deltoidal hexecontahedron * Medial disdyakis triacontahedron * Medial hexagonal hexecontahedron * Medial icosacronic hexecontahedron * Medial inverted pentagonal hexecontahedron * Medial pentagonal hexecontahedron * Medial rhombic triacontahedron * Hexahemioctacron * Hemipolyhedron * Octahemioctacron * Rhombicosacron * Small complex icosidodecahedron * Small ditrigonal dodecacronic hexecontahedron * Small dodecacronic hexecontahedron * Small dodecahemicosacron * Small dodecahemidodecacron * Small dodecicosacron * Small hexacronic icositetrahedron * Small hexagonal hexecontahedron * Small hexagrammic hexecontahedron * Small icosacronic hexecontahedron * Small icosihemidodecacron * Small rhombidodecacron * Small rhombihexacron * Small stellapentakis dodecahedron * Small triambic icosahedron * Tetrahemihexacron

Honeycombs

; Convex uniform honeycomb *

Cubic honeycomb The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb (geometry), honeycomb) in Euclidean 3-space made up of cube, cubic cells. It has 4 cubes around every edge, and 8 cubes around each verte ...

Triangular prismatic honeycomb The triangular prismatic honeycomb or triangular prismatic cellulation is a space-filling tessellation (or honeycomb (geometry), honeycomb) in Euclidean 3-space. It is composed entirely of triangular prisms. It is constructed from a triangular ti ...

* Triangular-hexagonal prismatic honeycomb * Truncated hexagonal prismatic honeycomb * Truncated square prismatic honeycomb *

Rhombitriangular-hexagonal prismatic honeycomb The triangular prismatic honeycomb or triangular prismatic cellulation is a space-filling tessellation (or honeycomb (geometry), honeycomb) in Euclidean 3-space. It is composed entirely of triangular prisms. It is constructed from a triangular ti ...

* Omnitruncated triangular-hexagonal prismatic honeycomb * Snub triangular-hexagonal prismatic honeycomb * Snub square prismatic honeycomb ;Dual uniform honeycomb * Disphenoid tetrahedral honeycomb * Rhombic dodecahedral honeycomb ;Others * Trapezo-rhombic dodecahedral honeycomb * Weaire–Phelan structure ; Convex uniform honeycombs in hyperbolic space *

Order-4 dodecahedral honeycomb In hyperbolic geometry, the order-4 dodecahedral honeycomb is one of four compact regular polytope, regular space-filling tessellations (or honeycomb (geometry), honeycombs) of hyperbolic 3-space. With Schläfli symbol it has four regular dodeca ...

* Order-5 cubic honeycomb * Order-5 dodecahedral honeycomb * Icosahedral honeycomb

Other

* Apeirogonal prism * Apeirohedron * Bicupola *

Cupola In architecture, a cupola () is a relatively small, usually dome-like structure on top of a building often crowning a larger roof or dome. Cupolas often serve as a roof lantern to admit light and air or as a lookout. The word derives, via Ital ...

* Bifrustum * Boerdijk–Coxeter helix * Császár polyhedron * Flexible polyhedron * Goldberg polyhedron * Gyroelongated square bipyramid *

Heronian tetrahedron A Heronian tetrahedron (also called a Heron tetrahedron or perfect pyramid) is a tetrahedron whose edge lengths, face areas and volume are all integers. The faces must therefore all be Heronian triangles (named for Hero of Alexandria). Every Heroni ...

* Hexagonal bifrustum * Hexagonal truncated trapezohedron * Hill tetrahedron * Holyhedron * Infinite skew polyhedron * Jessen's icosahedron *

Near-miss Johnson solid In geometry, a near-miss Johnson solid is a strictly convex set, convex polyhedron whose face (geometry), faces are close to being regular polygons but some or all of which are not precisely regular. Thus, it fails to meet the definition of a John ...

* Pentagonal bifrustum * Polytetrahedron * Pyritohedron * Rhombic enneacontahedron *

Rhombic icosahedron The rhombic icosahedron is a polyhedron shaped like an Oblate spheroid, oblate sphere. Its 20 faces are Congruence (geometry), congruent golden rhombi; 3, 4, or 5 faces meet at each vertex. It has 5 faces (green on top figure) meeting at each of ...

* Rhombo-hexagonal dodecahedron *

* Scalenohedron * Schönhardt polyhedron * Square bifrustum * Square truncated trapezohedron * Szilassi polyhedron * Tetradecahedron * Tetradyakis hexahedron * Tetrated dodecahedron * Triangular bifrustum * Triaugmented triangular prism * Truncated rhombic dodecahedron * Truncated trapezohedron * Truncated triakis tetrahedron * Tridyakis icosahedron *

* Regular skew polyhedron * Waterman polyhedron * Wedge

Regular and uniform compound polyhedra

;

Polyhedral compound In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common Centroid, centre. They are the three-dimensional analogs of star polygon#Regular compounds, polygonal compounds such as the hexagram. The oute ...

and

Uniform polyhedron compound In geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra, in an arrangement that is also uniform, i.e. the symmetry group of the compound acts t ...

Compound of cube and octahedron The compound of cube and octahedron is a polyhedron which can be seen as either a polyhedral stellation or a Polyhedron compound, compound. Construction The 14 Cartesian coordinates of the vertices of the compound are. : 6: (±2, 0, 0), ( 0, ± ...

* Compound of dodecahedron and icosahedron * Compound of eight octahedra with rotational freedom *

Compound of eight triangular prisms This uniform polyhedron compound is a symmetric arrangement of 8 triangular prisms, aligned in pairs with the axes of three-fold rotational symmetry of an octahedron In geometry, an octahedron (: octahedra or octahedrons) is any polyhedron ...

Compound of five cubes The compound of five cubes is one of the five regular polyhedral compounds. It was first described by Edmund Hess in 1876. Its vertices are those of a regular dodecahedron. Its edges form pentagrams, which are the stellations of the pentag ...

Compound of great icosahedron and great stellated dodecahedron There are two different compounds of great icosahedron and great stellated dodecahedron: one is a dual compound and a stellation of the great icosidodecahedron, the other is a stellation of the icosidodecahedron. Dual compound It can be seen ...

* Compound of six cubes with rotational freedom *

Compound of six decagonal prisms This uniform polyhedron compound is a symmetric arrangement of 6 decagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron. Cartesian coordinates Cartesian coordinates for the vertices of this compound are all th ...

Four dimensions

;

Four-dimensional space Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called ''dimensions'' ...

4-polytope In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: Vertex (geometry), vertices, Edge (geo ...

– general term for a four dimensional polytope ;

Regular 4-polytope In mathematics, a regular 4-polytope or regular polychoron is a regular polytope, regular 4-polytope, four-dimensional polytope. They are the four-dimensional analogues of the Regular polyhedron, regular polyhedra in three dimensions and the regul ...

5-cell In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol . It is a 5-vertex four-dimensional space, four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, hypertetrahedron, pentachoron, pentatope, pe ...

Tesseract In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six ...

, 16-cell,

24-cell In four-dimensional space, four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also called C24, or the icositetrachoron, octaplex (short for "octa ...

120-cell In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also called a C120, dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron, hec ...

600-cell In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also known as the C600, hexacosichoron and hexacosihedroid. It is also called a tetraplex (abbreviated from ...

; Abstract regular polytope * 11-cell, 57-cell ; Regular star 4-polytope * Icosahedral 120-cell, Small stellated 120-cell, Great 120-cell, Grand 120-cell, Great stellated 120-cell, Grand stellated 120-cell, Great grand 120-cell, Great icosahedral 120-cell, Grand 600-cell, Great grand stellated 120-cell ;

Uniform 4-polytope In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedron, uniform polyhedra, and faces are regular polygons. There are 47 non-Prism (geometry), prism ...

* Rectified 5-cell, Truncated 5-cell, Cantellated 5-cell, Runcinated 5-cell * Rectified tesseract, Truncated tesseract, Cantellated tesseract, Runcinated tesseract * Rectified 16-cell, Truncated 16-cell *

Rectified 24-cell In geometry, the rectified 24-cell or rectified icositetrachoron is a uniform 4-dimensional polytope (or uniform 4-polytope), which is bounded by 48 cell (mathematics), cells: 24 cubes, and 24 cuboctahedron, cuboctahedra. It can be obtained by Rec ...

, Truncated 24-cell, Cantellated 24-cell, Runcinated 24-cell,

Snub 24-cell In geometry, the snub 24-cell or snub disicositetrachoron is a convex uniform 4-polytope composed of 120 regular Tetrahedron, tetrahedral and 24 Regular icosahedron, icosahedral cell (mathematics), cells. Five tetrahedra and three icosahedra meet ...

* Rectified 120-cell, Truncated 120-cell, Cantellated 120-cell, Runcinated 120-cell *

Rectified 600-cell In geometry, the Rectification (geometry), rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cell (mathematics), cells. Each edge has two octahedra and one icosahedron ...

Honeycombs

* Tesseractic honeycomb * 24-cell honeycomb * Snub 24-cell honeycomb * Rectified 24-cell honeycomb * Truncated 24-cell honeycomb * 16-cell honeycomb * 5-cell honeycomb * Omnitruncated 5-cell honeycomb * Truncated 5-cell honeycomb * Omnitruncated 5-simplex honeycomb

Five dimensions

;

Five-dimensional space A five-dimensional (5D) space is a mathematical or physical concept referring to a space (mathematics), space that has five independent dimensions. In physics and geometry, such a space extends the familiar three spatial dimensions plus time ( ...

, 5-polytope and

uniform 5-polytope In geometry, a uniform 5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope Facet (geometry), facets. The complete set of convex uniform 5-polytopes ...

* 5-simplex, Rectified 5-simplex, Truncated 5-simplex, Cantellated 5-simplex, Runcinated 5-simplex, Stericated 5-simplex * 5-demicube, Truncated 5-demicube, Cantellated 5-demicube, Runcinated 5-demicube * 5-cube, Rectified 5-cube, Truncated 5-cube, Cantellated 5-cube, Runcinated 5-cube, Stericated 5-cube * 5-orthoplex, Rectified 5-orthoplex, Truncated 5-orthoplex, Cantellated 5-orthoplex, Runcinated 5-orthoplex ; Prismatic uniform 5-polytope * 5-cell prism, Rectified 5-cell prism, Truncated 5-cell prism, Cantellated 5-cell prism, Runcinated 5-cell prism, Bitruncated 5-cell prism, Cantitruncated 5-cell prism, Runcitruncated 5-cell prism, Omnitruncated 5-cell prism * Tesseractic prism, Rectified tesseractic prism, Truncated tesseractic prism, Cantellated tesseractic prism, Runcinated tesseractic prism, Bitruncated tesseractic prism, Cantitruncated tesseractic prism, Runcitruncated tesseractic prism, Omnitruncated tesseractic prism * 16-cell prism, Truncated 16-cell prism, Runcitruncated 16-cell prism * 24-cell prism, rectified 24-cell prism, truncated 24-cell prism, cantellated 24-cell prism, runcinated 24-cell prism, bitruncated 24-cell prism, cantitruncated 24-cell prism, runcitruncated 24-cell prism, omnitruncated 24-cell prism, snub 24-cell prism * 120-cell prism, Rectified 120-cell prism, Truncated 120-cell prism, Cantellated 120-cell prism, Runcinated 120-cell prism, Bitruncated 120-cell prism, Cantitruncated 120-cell prism, Runcitruncated 120-cell prism, Omnitruncated 120-cell prism * 600-cell prism, Rectified 600-cell prism, Truncated 600-cell prism, Cantellated 600-cell prism, Cantitruncated 600-cell prism, Runcitruncated 600-cell prism * Grand antiprism prism

Honeycombs

* 5-cubic honeycomb * 5-simplex honeycomb * Truncated 5-simplex honeycomb * 5-demicubic honeycomb

Six dimensions

; Six-dimensional space, 6-polytope and uniform 6-polytope * 6-simplex, Rectified 6-simplex, Truncated 6-simplex, Cantellated 6-simplex, Runcinated 6-simplex, Stericated 6-simplex, Pentellated 6-simplex * 6-demicube, Truncated 6-demicube, Cantellated 6-demicube, Runcinated 6-demicube, Stericated 6-demicube *6-cube, Rectified 6-cube, Truncated 6-cube, Cantellated 6-cube, Runcinated 6-cube, Stericated 6-cube, Pentellated 6-cube *6-orthoplex, Rectified 6-orthoplex, Truncated 6-orthoplex, Cantellated 6-orthoplex, Runcinated 6-orthoplex, Stericated 6-orthoplex *1 22 polytope, 1₂₂ polytope, 2 21 polytope, 2₂₁ polytope

Honeycombs

*6-cubic honeycomb *6-simplex honeycomb *6-demicubic honeycomb *2 22 honeycomb, 2₂₂ honeycomb

Seven dimensions

;Seven-dimensional space, uniform 7-polytope *7-simplex, Rectified 7-simplex, Truncated 7-simplex, Cantellated 7-simplex, Runcinated 7-simplex, Stericated 7-simplex, Pentellated 7-simplex, Hexicated 7-simplex *7-demicube, Truncated 7-demicube, Cantellated 7-demicube, Runcinated 7-demicube, Stericated 7-demicube, Pentellated 7-demicube *7-cube, Rectified 7-cube, Truncated 7-cube, Cantellated 7-cube, Runcinated 7-cube, Stericated 7-cube, Pentellated 7-cube, Hexicated 7-cube *7-orthoplex, Rectified 7-orthoplex, Truncated 7-orthoplex, Cantellated 7-orthoplex, Runcinated 7-orthoplex, Stericated 7-orthoplex, Pentellated 7-orthoplex, Hexicated 7-orthoplexes, Hexicated 7-orthoplex *1 32 polytope, 1₃₂ polytope, 2 31 polytope, 2₃₁ polytope, 3 21 polytope, 3₂₁ polytope

Honeycombs

*7-cubic honeycomb *7-demicubic honeycomb *3 31 honeycomb, 3₃₁ honeycomb, 1 33 honeycomb, 1₃₃ honeycomb

Eight dimension

;Eight-dimensional space, uniform 8-polytope *8-simplex, Rectified 8-simplex, Truncated 8-simplex, Cantellated 8-simplex, Runcinated 8-simplex, Stericated 8-simplex, Pentellated 8-simplex, Hexicated 8-simplex, Heptellated 8-simplex *8-demicube, Truncated 8-demicube, Cantellated 8-demicube, Runcinated 8-demicube, Stericated 8-demicube, Pentellated 8-demicube, Hexicated 8-demicube *8-cube, Rectified 8-cube, Truncated 8-cube, Cantellated 8-cube, Runcinated 8-cube, Stericated 8-cube, Pentellated 8-cube, Hexicated 8-cube, Heptellated 8-cube *8-orthoplex, Rectified 8-orthoplex, Truncated 8-orthoplex, Cantellated 8-orthoplex, Runcinated 8-orthoplex, Stericated 8-orthoplex, Pentellated 8-orthoplex, Hexicated 8-orthoplex, *1 42 polytope, 1₄₂ polytope, 2 41 polytope, 2₄₁ polytope, 4 21 polytope, 4₂₁ polytope, Truncated 4 21 polytope, Truncated 4₂₁ polytope, Truncated 2 41 polytope, Truncated 2₄₁ polytope, Truncated 1 42 polytope, Truncated 1₄₂ polytope, Cantellated 4 21 polytope, Cantellated 4₂₁ polytope, Cantellated 2 41 polytope, Cantellated 2₄₁ polytope, Runcinated 4 21 polytope, Runcinated 4₂₁ polytope

Honeycombs

*8-cubic honeycomb *8-demicubic honeycomb *5 21 honeycomb, 5₂₁ honeycomb, 2 51 honeycomb, 2₅₁ honeycomb, 1 52 honeycomb, 1₅₂ honeycomb

Nine dimensions

;9-polytope *9-simplex *9-demicube *9-cube *9-orthoplex

Hyperbolic honeycombs

*E9 honeycomb, E₉ honeycomb

Ten dimensions

;10-polytope *10-cube, 10-simplex *10-demicube *10-cube *10-simplex, 10-orthoplex

Dimensional families

;Regular polytope and List of regular polytopes *Simplex *Hypercube *Cross-polytope ;Uniform polytope *Demihypercube *Uniform 1 k2 polytope, Uniform 1_''k''2 polytope *Uniform 2 k1 polytope, Uniform 2_''k''1 polytope *Uniform k 21 polytope, Uniform ''k''₂₁ polytope ;Honeycombs *Hypercubic honeycomb *Alternated hypercubic honeycomb

Geometric operators

*Rectification (geometry) *Truncation (geometry) *Bitruncation *Cantellation *Runcination *Sterication *Omnitruncation *Expansion (geometry) *Snub (geometry) *Alternation (geometry) *Dual polyhedron *Gyration (geometry) *Elongation (geometry) *Augmentation (geometry) *Diminishment (geometry) *Greatening (geometry) *Aggrandizement (geometry) *Stellation *Kleetope *Conway polyhedron notation

Polytope elements

Polygon (2-polytope)

Polyhedron (3-polytope)

Polychoron (4-polytope)

5-polytope

Other

Two dimensional (polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...s)

Star polygon In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, Decagram (geometry)#Related figures, certain notable ones can ...s

Families

Tilings

Three dimensional (polyhedra In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary su ...)

Regular

Archimedean solids

Prisms and antiprisms

Catalan solids

Bipyramids and Trapezohedron

Uniform star polyhedra

Uniform prismatic star polyhedra

Johnson solids

Dual uniform star polyhedra

Honeycombs

Other

Regular and uniform compound polyhedra

Four dimensions

Honeycombs

Five dimensions

Honeycombs

Six dimensions

Honeycombs

Seven dimensions

Honeycombs

Eight dimension

Honeycombs

Nine dimensions

Hyperbolic honeycombs

Ten dimensions

Dimensional families

Geometric operators

See also

Two dimensional (
polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...
s)

Star polygon In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, Decagram (geometry)#Related figures, certain notable ones can ...
s

Three dimensional (
polyhedra In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary su ...
)