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Hexecontahedron

From Wikipedia, the free encyclopedia

Pentakis dodecahedron	Deltoidal hexecontahedron
Pentagonal hexecontahedron	Triakis icosahedron
Rhombic hexecontahedron	Small hexagonal hexecontahedron

In geometry, a hexecontahedron (or hexacontahedron^[1]) is a polyhedron with 60 faces. There are many symmetric forms, and the ones with highest symmetry have icosahedral symmetry:

Four Catalan solids, convex:

Pentakis dodecahedron - isosceles triangles
Deltoidal hexecontahedron - kites
Pentagonal hexecontahedron - pentagons
Triakis icosahedron - isosceles triangles

Concave

Rhombic hexecontahedron - rhombi

27 uniform star-polyhedral duals: (self-intersecting)

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References

^ "Greek numerical prefixes".

Weisstein, Eric W. "Hexecontahedron". MathWorld.

v t e Polyhedra
Listed by number of faces and type
1–10 faces	Monohedron Dihedron Trihedron Tetrahedron Pentahedron Hexahedron Heptahedron Octahedron Enneahedron Decahedron
11–20 faces	Hendecahedron Dodecahedron Tridecahedron Tetradecahedron Pentadecahedron Hexadecahedron Heptadecahedron Octadecahedron Enneadecahedron Icosahedron
>20 faces	Icositetrahedron (24) Triacontahedron (30) Icosidodecahedron (32) Hexoctahedron (48) Hexecontahedron (60) Enneacontahedron (90) Hectotriadiohedron (132) Apeirohedron (∞)
elemental things	face edge vertex uniform polyhedron (two infinite groups and 75) regular polyhedron (9) quasiregular polyhedron (7) semiregular polyhedron (two infinite groups and 59)
convex polyhedron	Platonic solid (5) Archimedean solid (13) Catalan solid (13) Johnson solid (92)
non-convex polyhedron	Kepler–Poinsot polyhedron (4) Star polyhedron (infinite) Uniform star polyhedron (57)
prismatoid‌s	prism antiprism frustum cupola wedge pyramid parallelepiped

This page was last edited on 1 June 2022, at 01:13

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