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Disdyakis triacontahedron
Type	Catalan
Face polygon	scalene triangle
Faces	120
Edges	180
Vertices	62 = 12 + 20 + 30
Face configuration	V4.6.10
Symmetry group	icosahedral (Ih)
Dual polyhedron	truncated icosidodecahedron
Properties	convex, face-uniform

A disdyakis triacontahedron, or hexakis icosahedron is the Catalan solid whose Archimedean dual is the truncated icosidodecahedron. As such it is face uniform but with irregular face polygons. It looks a bit like 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. Side lengths for r=12: s1=4.35411996 s2=6.55839670 s3=7.69022184 (Calculated by Garrith McLean)

See also

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• Disdyakis dodecahedron

Catalan solids

Triacontaedro disdiakis | Hexaki icosaèdre | 六方二十面体 | Triacontaedro disdiakis