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Encyclopedia > Rhombicosidodecahedron
Small rhombicosidodecahedron Type Archimedean solid
Elements F=62, E=120, V=60 (χ=2)
Faces by sides 20{3}+30{4}+12{5}
Schläfli symbol $rbegin{Bmatrix} 3 5 end{Bmatrix}$
Wythoff symbol 3 5 | 2
Coxeter-Dynkin     Symmetry Ih
References U27, C30, W14
Dual Deltoidal hexecontahedron
Properties Semiregular convex Vertex figure
3.4.5.4

The name rhombicosidodecahedron refers to the fact that the 30 square faces lie in the same planes as the 30 faces of the rhombic triacontahedron which is dual to the icosidodecahedron. The Rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. ... An icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. ...

It can also called a cantellated dodecahedron or a cantellated icosahedron from truncation operations of the uniform polyhedron. A cantellated cube - Red faces are reduced. ... A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ...

## Contents

If you blow up an icosahedron by moving the faces away from the origin the right amount, without changing the orientation or size of the faces, and do the same to its dual dodecahedron, and patch the square holes in the result, you get a rhombicosadodecahedron. Therefore, it has the same number of triangles as an icosahedron and the same number of pentagons as a dodecahedron, with a square for each edge of either. An icosahedron noun (plural: -drons, -dra ) is a polyhedron having 20 faces, but usually a regular icosahedron is implied, which has equilateral triangles as faces. ... In mathematics, the origin of a coordinate system is the point where the axes of the system intersect. ... Look up Dual in Wiktionary, the free dictionary A dual is a pair or a grouping of two. ... A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex. ...

The rhombicosidodecahedron shares the vertex arrangement with the small stellated truncated dodecahedron, and with the uniform compounds of 6 or 12 pentagrammic prisms. In geometry, the small stellated truncated dodecahedron is a nonconvex uniform polyhedron, indexed as U58. ... In geometry, the pentagrammic prism is the first in an infinite set of concave prisms formed by square sides and two regular star polygon caps, in this case two pentagrams. ...

The Zometool kits for making geodesic domes and other polyhedra use slotted balls as connectors. The balls are "expanded" small rhombicosidodecahedra, with the squares replaced by rectangles. The expansion is chosen so that the resulting rectangles are golden rectangles. Zometool logo The term zome is used in two senses, though both are related. ... The Montreal BiosphÃ¨re, formerly the American Pavilion of Expo 67, by R. Buckminster Fuller, on ÃŽle Sainte-HÃ©lÃ¨ne, Montreal, Canada A geodesic dome is an almost spherical structure based on a network of struts arranged on great circles (geodesics) lying approximately on the surface of a sphere. ...

## Cartesian coordinates

Cartesian coordinates for the vertices of a rhombicosidodecahedron centered at the origin are Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...

(±1, ±1, ±τ3),
(±τ3, ±1, ±1),
(±1, ±τ3, ±1),
(±τ2, ±τ, ±2τ),
(±2τ, ±τ2, ±τ),
(±τ, ±2τ, ±τ2),
(±(2+τ), 0, ±τ2),
(±τ2, ±(2+τ), 0),
(0, ±τ2, ±(2+τ)),

where τ = (1+√5)/2 is the golden ratio. The golden section is a line segment sectioned into two according to the golden ratio. ...

Spinning truncated tetrahedron, made by me using POV-Ray, see image:poly. ... A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex. ... An icosahedron noun (plural: -drons, -dra ) is a polyhedron having 20 faces, but usually a regular icosahedron is implied, which has equilateral triangles as faces. ... An icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. ... The rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. ... The truncated icosidodecahedron, or great rhombicosidodecahedron, is an Archimedean solid. ... Results from FactBites:

 Rhombicosidodecahedron - Wikipedia, the free encyclopedia (229 words) The rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid. The name rhombicosidodecahedron refers to the fact that the 30 square faces lie in the same planes as the 30 faces of the rhombic triacontahedron which is dual to the icosidodecahedron. Cartesian coordinates for the vertices of a rhombicosidodecahedron centered at the origin are
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