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The pentakis icosidodecahedron is a convex polyhedron with 80 triangular faces, 120 edges, and 42 vertices. It a dual of the truncated rhombic triacontahedron. Its name comes from a topological construction from the icosidodecahedron with the kis operator applied to the pentagonal faces. In this construction, all the vertices are assumed to be the same distance from the center, while in general icosahedral symmetry can be maintained even with the 12 order-5 vertices at a different distance from the center as the other 30. It can also be topologically constructed from the icosahedron, dividing each triangular face into 4 triangles by adding mid-edge vertices. From this construction, all 80 triangles will be equilateral, but faces will be coplanar. == Related polyhedra == File:Pentakis icosidodecahedron net.png|Net File:Icosidodecahedron.png|Icosidodecahedron File:Icosahedron subdivided.png|Icosahedron with each face subdivided into four equilateral triangles. File:Pentakisdodecahedron.jpg|Pentakis dodecahedron is a slightly smaller Catalan solid which has 60 isosceles triangle faces, 90 edges (2 types), and 32 vertices (2 types). File:StellaTripentakisIcosidodecahedron.png|Tripentakis icosidodecahedron, the Kleetope of the icosahedron, can be obtained by raising low pyramids on each equilateral triangular face on a pentakis icosidodecahedron. It has 120 isosceles triangle faces (2 types), 180 edges (3 types) and 62 vertices (3 types). File:Small icosihemidodecahedron.png|The nonconvex small icosihemidodecahedron looks like a pentakis icosidodecahedron with inverted pentagonal pyramids meeting at the polyhedron center. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pentakis icosidodecahedron」の詳細全文を読む スポンサード リンク
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