This is a list of

two-dimensional In mathematics, a plane is a Euclidean ( flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as ...

geometric shapes in Euclidean and other

geometries This is a list of geometry topics. Types, methodologies, and terminologies of geometry. * Absolute geometry * Affine geometry * Algebraic geometry * Analytic geometry * Archimedes' use of infinitesimals * Birational geometry * Complex geomet ...

. For mathematical objects in more dimensions, see

list of mathematical shapes Following is a list of some mathematically well-defined shapes. Algebraic curves *Cubic plane curve *Quartic plane curve Rational curves Degree 2 *Conic sections *Unit circle *Unit hyperbola Degree 3 *Folium of Descartes *Cissoid of Diocles * ...

. For a broader scope, see list of shapes.

Generally composed of straight line segments

Angle In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles a ...

Balbis In geometry, a balbis is a geometric shape that can be colloquially defined as a single (primary) line that is terminated by a (secondary) line at one endpoint and by a (secondary) line at the other endpoint. The terminating secondary lines are a ...

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. Polyg ...

Constructible polygon In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinite ...

Convex polygon In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a ...

Cyclic polygon In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every poly ...

Equiangular polygon In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon. Isogonal polygons are equiangular polygons whic ...

Equilateral polygon In geometry, an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, an equilateral polygon does not need to also be equiangular (have all angles equal), but if it does then it is a regular polygon ...

* Penrose tile *

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 triangle ...

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

Simple polygon In geometry, a simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a flat shape consisting of straight, non-intersecting line segments or "sides" that are joined pairwise to form a single closed path. If ...

Tangential polygon In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an ''incircle''). This is a circle that is tangent to each of the polygon's sides. The dual pol ...

Polygons with specific numbers of sides

* Henagon – 1 side *

Digon In geometry, a digon is a polygon with two sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be easily visu ...

– 2 sides *

Triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ...

– 3 sides **

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 triangle's ang ...

Equilateral triangle In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each oth ...

** Heptagonal triangle ** Isosceles triangle ***

Golden Triangle Golden Triangle may refer to: Places Asia * Golden Triangle (Southeast Asia), named for its opium production * Golden Triangle (Yangtze), China, named for its rapid economic development * Golden Triangle (India), comprising the popular tourist ...

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 triangle's ang ...

Rational triangle An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers. A rational triangle can be defined as one having all sides with rational length; any such rational triangle can be integrally rescaled (ca ...

Right triangle A right triangle (American English) or right-angled triangle ( British), or more formally an orthogonal triangle, formerly called a rectangled triangle ( grc, ὀρθόσγωνία, lit=upright angle), is a triangle in which one angle is a right a ...

***

30-60-90 triangle A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45° ...

***

Isosceles right triangle A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45° ...

***

Kepler triangle A Kepler triangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is \sqrt\varphi where \varphi=(1+\sqrt)/2 is the golden ratio, and the progression can be written: or approximately . Squares ...

Scalene triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear ...

Quadrilateral In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, ...

– 4 sides **

Cyclic quadrilateral In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the ''circumcircle'' or ''circumscribed circle'', and the vertices are said to be ''c ...

Kite A kite is a tethered heavier-than-air or lighter-than-air craft with wing surfaces that react against the air to create lift and drag forces. A kite consists of wings, tethers and anchors. Kites often have a bridle and tail to guide the fac ...

** Parallelogram *** Rhombus (equilateral parallelogram) **** Lozenge (shape), Lozenge *** Rhomboid *** Rectangle *** Square (geometry), Square (regular quadrilateral) ** Tangential quadrilateral ** Trapezoid *** Isosceles trapezoid * Pentagon – 5 sides * Hexagon – 6 sides ** Lemoine hexagon * Heptagon – 7 sides * Octagon – 8 sides * Nonagon – 9 sides * Decagon – 10 sides * Hendecagon – 11 sides * Dodecagon – 12 sides * Tridecagon – 13 sides * Tetradecagon – 14 sides * Pentadecagon – 15 sides * Hexadecagon – 16 sides * Heptadecagon – 17 sides * Octadecagon – 18 sides * Enneadecagon – 19 sides * Icosagon – 20 sides * Icosikaihenagon - 21 sides * Icosikaidigon - 22 sides * Icositrigon - 23 sides * Icositetragon - 24 sides * Icosikaipentagon - 25 sides * Icosikaihexagon - 26 sides * Icosikaiheptagon - 27 sides * Icosikaioctagon - 28 sides * Icosikaienneagon - 29 sides * Triacontagon - 30 sides * Tetracontagon - 40 sides * Pentacontagon - 50 sides * Hexacontagon - 60 sides * Heptacontagon - 70 sides * Octacontagon - 80 sides * Enneacontagon - 90 sides * Hectogon - 100 sides * Dihectogon - 200 sides * Trihectogon - 300 sides * Tetrahectogon - 400 sides * Pentahectogon - 500 sides * Hexahectogon - 600 sides * Heptahectogon - 700 sides * Octahectogon - 800 sides * Enneahectogon - 900 sides * Chiliagon - 1,000 sides * Myriagon - 10,000 sides * Megagon - 1,000,000 sides * Star polygon – there are multiple types of stars ** Pentagram - star polygon with 5 sides ** Hexagram – star polygon with 6 sides *** Star of David (example) ** Heptagram – star polygon with 7 sides ** Octagram – star polygon with 8 sides *** Star of Lakshmi (example) ** Enneagram (geometry), Enneagram - star polygon with 9 sides ** Decagram (geometry), Decagram - star polygon with 10 sides ** Hendecagram - star polygon with 11 sides ** Dodecagram - star polygon with 12 sides * Apeirogon - generalized polygon with countably infinite set of sides

Curved

Composed of circular arcs

* annulus (mathematics), Annulus * Arbelos * Circle ** Archimedes' twin circles ** Bankoff circle ** Circular triangle *** Reuleaux triangle ** Circumcircle ** disc (mathematics), Disc ** Incircle and excircles of a triangle ** Nine-point circle * Circular sector * Circular segment * Crescent * lens (geometry), Lens, vesica piscis (fish bladder) * Lune (mathematics), Lune * Quatrefoil * Reuleaux polygon ** Reuleaux triangle * Salinon * Semicircle * tomahawk (geometric shape), Tomahawk * Trefoil * Triquetra * Heart shape, Heart

Not composed of circular arcs

* Archimedean spiral * Astroid * Cardioid * deltoid curve, Deltoid * Ellipse * Heartagon * Various lemniscates * Oval (geometry), Oval ** Cartesian oval ** Cassini oval ** Oval of Booth * Ovoid – similar to an oval * Superellipse * Taijitu * Tomoe * Magatama

References