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The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
3D model of a rhombic triacontahedron. The rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron.
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.
Small dodecahemidodecacron (Dual of small dodecahemidodecacron) — V(5.10. 5 / 4 .10) π − π / 5 144° Small icosihemidodecacron (Dual of small icosihemidodecacron) — V(3.10. 3 / 2 .10) π − π / 5 144° Great dodecahemicosacron (Dual of great dodecahemicosahedron) — V(5.6. 5 / 4 .6) π − π ...
[1] [2] 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.
Download as PDF; Printable version; In other projects ... Truncated small rhombicosidodecahedron; ... and a rhombic triacontahedron. [1] Related polyhedra
Four numbering schemes for the uniform polyhedra are in common use, distinguished by letters: [C] Coxeter et al., 1954, showed the convex forms as figures 15 through 32; three prismatic forms, figures 33–35; and the nonconvex forms, figures 36–92.
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