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Gyrate Rhombicosidodecahedron
In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids (). It is also a canonical polyhedron. Related polyhedron It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees. They have the same faces around each vertex, but vertex configurations along the rotation become a different order, . Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are: * The parabigyrate rhombicosidodecahedron () where two opposing cupolae are rotated; * The metabigyrate rhombicosidodecahedron () where two non-opposing cupolae are rotated; * And the trigyrate rhombicosidodecahedron In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (). It contains 20 triangles, 30 squares and 12 pentagons. It is also a Midsphere#Canonical polyhedron, canonical polyhedron. It can be constructed as a rhombicosi ... () where three cupolae are rotated. External links ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigyrate Rhombicosidodecahedron
In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (). It contains 20 triangles, 30 squares and 12 pentagons. It is also a canonical polyhedron. It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae rotated through 36 degrees. Related Johnson solids are: * The gyrate rhombicosidodecahedron () where one cupola is rotated; * The parabigyrate rhombicosidodecahedron () where two opposing cupolae are rotated; * And the metabigyrate rhombicosidodecahedron () where two non-opposing cupolae are rotated. References *Norman W. Johnson Norman Woodason Johnson () was a mathematician at Wheaton College, Norton, Massachusetts. Early life and education Norman Johnson was born on in Chicago. His father had a bookstore and published a local newspaper. Johnson earned his unde ..., "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 sol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabigyrate Rhombicosidodecahedron
In geometry, the parabigyrate rhombicosidodecahedron is one of the Johnson solids (). It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron. Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are: * The gyrate rhombicosidodecahedron () where only one cupola is rotated; * The metabigyrate rhombicosidodecahedron () where two non-opposing cupolae are rotated; * And the trigyrate rhombicosidodecahedron In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (). It contains 20 triangles, 30 squares and 12 pentagons. It is also a canonical polyhedron. It can be constructed as a rhombicosidodecahedron with three pentag ... () where three cupolae are rotated. External links * Johnson solids {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metabigyrate Rhombicosidodecahedron
In geometry, the metabigyrate rhombicosidodecahedron is one of the Johnson solids (). It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron. Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are: * The gyrate rhombicosidodecahedron () where only one cupola is rotated; * The parabigyrate rhombicosidodecahedron () where two opposing cupolae are rotated; * And the trigyrate rhombicosidodecahedron In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (). It contains 20 triangles, 30 squares and 12 pentagons. It is also a canonical polyhedron. It can be constructed as a rhombicosidodecahedron with three pentag ... () where three cupolae are rotated. External links * World of Polyhedra - metabigyrate rhombicosidodecahedron(interactive rotatable wireframe applet) Johnson solids {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentagonal Cupola
In geometry, the pentagonal cupola is one of the Johnson solids (). It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 pentagon, and 1 decagon. Formulae The following formulae for volume, surface area and circumradius can be used if all faces are regular, with edge length ''a'':Stephen Wolfram,Pentagonal cupola from Wolfram Alpha. Retrieved April 11, 2020. :V=\left(\frac\left(5+4\sqrt\right)\right)a^3\approx2.32405a^3, :A=\left(\frac\left(20+5\sqrt+\sqrt\right)\right)a^2\approx16.57975a^2, :R=\left(\frac\sqrt\right)a\approx2.23295a. The height of the pentagonal cupola is :h = \sqrta \approx 0.52573a. Related polyhedra Dual polyhedron The dual of the pentagonal cupola has 10 triangular faces and 5 kite faces: Other convex cupolae Crossed pentagrammic cupola In geometry, the crossed pentagrammic cupola is one of the nonconvex Johnson solid isomorphs, being topologically identical to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gyrate Rhombicosidodecahedron Color
Gyrate may refer to: * Gyrus, a ridge on the cerebral cortex * Gyration, a type of rotation Music * ''Gyrate'' (album), a 1980 album by Pylon * "Gyrate", song by Pylon from Chomp (album) ''Chomp'' is the second studio album by Athens, Georgia band Pylon, released in 1983. It was re-released in 2009 via DFA Records. Critical reception ''Trouser Press'' called the album "more ambitious in scope" than the debut, writing that it "i ... * "Gyrate", song by WizKid from Made in Lagos {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombicosidodecahedron
In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square (geometry), square faces, 12 regular pentagonal faces, 60 vertex (geometry), vertices, and 120 edge (geometry), edges. Names Johannes Kepler in Harmonices Mundi (1618) named this polyhedron a ''rhombicosidodecahedron'', being short for ''truncated icosidodecahedral rhombus'', with ''icosidodecahedral rhombus'' being his name for a rhombic triacontahedron. There are different truncations of a rhombic triacontahedron into a topology, topological rhombicosidodecahedron: Prominently its rectification (geometry), rectification (left), the one that creates the uniform solid (center), and the rectification of the dual icosidodecahedron (right), which is the core of the dual compound. It can also be called an ''Expansion (geometry), expanded'' or ''Cantellation (geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Small Rhombicosidodecahedron
In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges. Names Johannes Kepler in Harmonices Mundi (1618) named this polyhedron a ''rhombicosidodecahedron'', being short for ''truncated icosidodecahedral rhombus'', with ''icosidodecahedral rhombus'' being his name for a rhombic triacontahedron. There are different truncations of a rhombic triacontahedron into a topological rhombicosidodecahedron: Prominently its rectification (left), the one that creates the uniform solid (center), and the rectification of the dual icosidodecahedron (right), which is the core of the dual compound. It can also be called an '' expanded'' or '' cantellated'' dodecahedron or icosahedron, from truncation operations on either uniform polyhedron. Dimensions For a r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertex Configuration
In geometry, a vertex configurationCrystallography of Quasicrystals: Concepts, Methods and Structures by Walter Steurer, Sofia Deloudi, (2009) pp. 18–20 and 51–53Physical Metallurgy: 3-Volume Set, Volume 1 edited by David E. Laughlin, (2014) pp. 16–20 is a shorthand notation for representing the of a or |
Johnson Solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), vertex. An example of a Johnson solid is the square-based Pyramid (geometry), pyramid with equilateral sides (square pyramid, ); it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform polyhedron, uniform (i.e., not Platonic solid, Archimedean solid, prism (geometry), uniform prism, or uniform antiprism) before they refer to it as a “Johnson solid”. As in any strictly convex solid, at least three faces meet at every vertex, and the total of their angles is less than 360 degrees. Since a regular polygon has angles at least 60 degrees, it follows that at most five faces meet at any vertex. The pentagonal pyramid () is an example that has a degree-5 vertex. Although there is no obvious restriction tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombicosidodecahedron
In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square (geometry), square faces, 12 regular pentagonal faces, 60 vertex (geometry), vertices, and 120 edge (geometry), edges. Names Johannes Kepler in Harmonices Mundi (1618) named this polyhedron a ''rhombicosidodecahedron'', being short for ''truncated icosidodecahedral rhombus'', with ''icosidodecahedral rhombus'' being his name for a rhombic triacontahedron. There are different truncations of a rhombic triacontahedron into a topology, topological rhombicosidodecahedron: Prominently its rectification (geometry), rectification (left), the one that creates the uniform solid (center), and the rectification of the dual icosidodecahedron (right), which is the core of the dual compound. It can also be called an ''Expansion (geometry), expanded'' or ''Cantellation (geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triaugmented Truncated Dodecahedron
In geometry, the triaugmented truncated dodecahedron is one of the Johnson solids (); of them, it has the greatest volume in proportion to the cube of the side length. As its name suggests, it is created by attaching three pentagonal cupolas () onto three nonadjacent decagonal faces of a truncated dodecahedron In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. Geometric relations This polyhedron can be formed from a regular dodecahedron by truncat .... External links * Johnson solids {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Midsphere
In geometry, the midsphere or intersphere of a polyhedron In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on ... is a sphere which is tangent to every Edge (geometry), edge of the polyhedron. That is to say, it touches any given edge at exactly one point. Not every polyhedron has a midsphere, but for every convex polyhedron there is a combinatorially equivalent polyhedron, the canonical polyhedron, that does have a midsphere. The radius of the midsphere is called the midradius. Examples The uniform polyhedron, uniform polyhedra, including the regular polyhedron, regular, Quasiregular polyhedron, quasiregular and Semiregular polyhedron, semiregular polyhedra and their Dual polyhedron, duals all have midspheres. In the regular polyhedra, the inscribed sphere, midsphere, and circumscribe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
