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It slightly resembles an inflated rhombic triacontahedron: if one replaces each face of the rhombic triacontahedron with a single vertex and four triangles in a regular fashion, one ends up with a disdyakis triacontahedron. That is, the disdyakis triacontahedron is the Kleetope of the rhombic triacontahedron.
3D model of a medial disdyakis triacontahedron. In geometry, the medial disdyakis triacontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform truncated dodecadodecahedron. It has 120 triangular faces.
Medial disdyakis triacontahedron; Medial hexagonal hexecontahedron; Medial icosacronic hexecontahedron; Medial inverted pentagonal hexecontahedron; Medial pentagonal hexecontahedron; Medial rhombic triacontahedron; Hexahemioctacron; Hemipolyhedron; Octahemioctacron; Rhombicosacron; Small complex icosidodecahedron; Small ditrigonal dodecacronic ...
Fifteen great circles represent the edges of a disdyakis triacontahedron, the dual of a truncated icosidodecahedron. Six more great circles represent the edges of an icosidodecahedron, and the last ten great circles come from the edges of the uniform star dodecadodecahedron, making pentagrams with vertices at the edge centers of the icosahedron.
3D model of a great disdyakis triacontahedron. The great disdyakis triacontahedron (or trisdyakis icosahedron) is a nonconvex isohedral polyhedron. It is the dual of the great truncated icosidodecahedron. Its faces are triangles.
Medial disdyakis triacontahedron; Medial hexagonal hexecontahedron; Medial icosacronic hexecontahedron; Medial inverted pentagonal hexecontahedron; Medial pentagonal hexecontahedron; Medial rhombic triacontahedron; Hexahemioctacron; Hemipolyhedron; Octahemioctacron; Rhombicosacron; Small complex icosidodecahedron; Small ditrigonal dodecacronic ...
triakis tetrahedron, triakis octahedron, tetrakis hexahedron, disdyakis dodecahedron, triakis icosahedron, pentakis dodecahedron, disdyakis triacontahedron; Simplicial tilings: Regular: triangular tiling; Laves tilings: tetrakis square tiling, triakis triangular tiling, kisrhombille tiling; Simplicial 4-polytopes include: convex regular 4-polytope
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.