Disdyakis triacontahedron
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Type	Catalan
Face polygon	scalene triangle
Faces	120
Edges	180
Vertices	62 = 12 + 20 + 30
Face configuration	4,6,10
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) Download high resolution version (812x847, 130 KB)Disdyakis triacontahedron, made by me using POV-Ray, see image:poly. ... Spinning disdyakis triacontahedron, made by me using POV-Ray, see image:poly. ... A rhombic dodecahedron In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... The symmetry group of an object (e. ... The icosahedral rotation group I with fundamental domain Apart from the two infinite series of prismatic and antiprismatic symmetry, rotational icosahedral symmetry or chiral icosahedral symmetry of chiral objects and full icosahedral symmetry or achiral icosahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the... In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ... The truncated icosidodecahedron, or great rhombicosidodecahedron, is an Archimedean solid. ... A rhombic dodecahedron In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. ... In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ... The truncated icosidodecahedron, or great rhombicosidodecahedron, is an Archimedean solid. ... The Rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. ...

See also

• disdyakis dodecahedron