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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.
It is a stellation of the rhombic triacontahedron, and can also be called small stellated triacontahedron. Its dual is the dodecadodecahedron . Its 24 vertices are all on the 12 axes with 5-fold symmetry (i.e. each corresponds to one of the 12 vertices of the icosahedron ).
Small stellated dodecahedron ... Rhombic triacontahedron ... ISBN 0-486-61480-8 (Table I: Regular Polytopes, (i) The nine regular polyhedra {p,q} in ordinary space)
A regular polyhedral compound can be defined as a compound which, like a regular polyhedron, is vertex-transitive, edge-transitive, and face-transitive.Unlike the case of polyhedra, this is not equivalent to the symmetry group acting transitively on its flags; the compound of two tetrahedra is the only regular compound with that property.
Vertex the (n−5)-face of the 5-polytope; Edge the (n−4)-face of the 5-polytope; Face the peak or (n−3)-face of the 5-polytope; Cell the ridge or (n−2)-face of the 5-polytope; Hypercell or Teron the facet or (n−1)-face of the 5-polytope
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure : not itself an element of a polytope, but a diagram showing how the elements meet.
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.
Toggle the table of contents. ... Faces: 122: 60 {4} 20 {6} 30 {8} 12 {10} Edges: 360 ... and a rhombic triacontahedron. [1] Related polyhedra