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Encyclopedia > Rhombicosidodecahedron
Small rhombicosidodecahedron
Rhombicosidodecahedron
(Click here for rotating model)
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 Image:CDW_ring.png Image:CDW_5.png Image:CDW_dot.png Image:CDW_3.png Image:CDW_ring.png
Symmetry Ih
References U27, C30, W14
Dual Deltoidal hexecontahedron
Properties Semiregular convex
Rhombicosidodecahedron
Vertex figure
3.4.5.4
A colored model
A colored model

The rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid. It has 20 regular triangular faces, 30 regular square faces, 12 regular pentagonal faces, 60 vertices and 120 edges. Download high resolution version (858x871, 113 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Spinning truncated tetrahedron, made by me using POV-Ray, see image:poly. ... In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ... It has been suggested that Vertex/Face/Edge relation in a convex polyhedron be merged into this article or section. ... In mathematics, the Schläfli symbol is a simple notation that gives a summary of some important properties of a particular regular polytope. ... In geometry, a Wythoff construction, named after mathematician Willem Abraham Wijthoff, is a method for constructing a uniform polyhedron or plane tiling. ... Coxeter groups in the plane with equivalent diagrams. ... Image File history File links CDW_ring. ... Image File history File links CDW_5. ... Image File history File links CDW_dot. ... Image File history File links CDW_3. ... Image File history File links CDW_ring. ... // List of symmetry groups on the sphere Spherical symmetry groups are also called point groups (in 3D). ... The icosahedral rotation group I with fundamental domain Apart from the two infinite series of prismatic and antiprismatic symmetry, rotational icosahedral symmetry or chiral icosahedral symmetry of chiral objects and full icosahedral symmetry or achiral icosahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the... A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ... A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ... H.S.M. Coxeter. ... This table contains an indexed list of the Uniform and stellated polyhedra from the book Polyhedron Models, by Magnus J. Wenninger. ... In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ... A deltoidal hexecontahedron is a catalan solid which looks a bit like an overinflated dodecahedron. ... Image File history File links Small_rhombicosidodecahedron_vertfig. ... In polyhedral geometry a vertex configuration is a short-hand notation for representing a vertex as the sequence of faces around a vertex. ... Image File history File links Download high resolution version (1000x1000, 289 KB) Licensing Robert Webb produced this image for Wikipedia upon my request, and offered the credit statement below: File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (1000x1000, 289 KB) Licensing Robert Webb produced this image for Wikipedia upon my request, and offered the credit statement below: File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Rhombicosidodecahedron_flat. ... Image File history File links Rhombicosidodecahedron_flat. ... Categories: Polyhedra | Stub ... In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... For other uses, see square. ... Look up pentagon in Wiktionary, the free dictionary. ...


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


Geometric relations

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 Biosphère, formerly the American Pavilion of Expo 67, by R. Buckminster Fuller, on Île Sainte-Hélène, 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. ...


See also

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. ...

References

  • Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X.  (Section 3-9)

This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...

External links


  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
  More results at FactBites »

 
 

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