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It has 14 regular faces (6 octagonal and 8 triangular), 36 edges, and 24 vertices. If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and δ S +1 , where δ S is the silver ratio, √ 2 +1.
Alternatively, if you expand each of five cubes by moving the faces away from the origin the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron ...
A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron , i.e., an Archimedean solid that is not only vertex-transitive but also edge-transitive . [ 1 ]
For example, a chamfered cube, cC, can be constructed as t 4 daC, as a rhombic dodecahedron, daC or jC, with its degree-4 vertices truncated. A lofted cube, lC is the same as t 4 kC . A quinto-dodecahedron, qD can be constructed as t 5 daaD or t 5 deD or t 5 oD , a deltoidal hexecontahedron , deD or oD , with its degree-5 vertices truncated.
The diagram is named for Victor Schlegel, who in 1886 introduced this tool for studying combinatorial and topological properties of polytopes. In dimension 3, a Schlegel diagram is a projection of a polyhedron into a plane figure; in dimension 4, it is a projection of a 4-polytope to 3-space.
The 5 Platonic solids are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively. The regular hexahedron is a cube . Table of polyhedra
In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, [1] great rhombicosidodecahedron, [2] [3] omnitruncated dodecahedron or omnitruncated icosahedron [4] is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces.
Faces by sides: 30{4}+20{6} Coxeter diagram (with extra double-covered pentagrams) (with extra double-covered pentagons) Wythoff symbol: 2 3 (5/4 5/2) | Symmetry group: I h, [5,3], *532 Index references: U 56, C 72, W 96: Dual polyhedron: Rhombicosacron: Vertex figure: 4.6.4/3.6/5 Bowers acronym: Ri