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disdyakis triacontahedron
In geometry, a disdyakis triacontahedron, hexakis icosahedron or kisrhombic triacontahedron〔Conway, Symmetries of things, p.284〕 is a Catalan solid with 120 faces and the dual to the Archimedean 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. That is, the disdyakis triacontahedron is the Kleetope of the rhombic triacontahedron. It also has the most faces among the Archimedean and Catalan solids, with the snub dodecahedron, with 92 faces, in second place.
If the bipyramids and the trapezohedra are excluded,
the disdyakis triacontahedron has the most faces of any other strictly convex polyhedron where every face of the polyhedron has the same shape.
==Symmetry==
The edges of the polyhedron projected onto a sphere form 15 great circles, and represent all 15 mirror planes of reflective ''Ih'' icosahedral symmetry, as shown in this image. Combining pairs of light and dark triangles define the fundamental domains of the nonreflective (''I'') icosahedral symmetry. The edges of a compound of five octahedra also represent the 10 mirror planes of icosahedral symmetry.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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