Icositetrahedron - Wikipedia

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Triakis octahedron	Tetrakis hexahedron
Deltoidal icositetrahedron	Pentagonal icositetrahedron

In geometry, an icositetrahedron^[1] is a polyhedron with 24 faces. There are many symmetric forms, and the ones with highest symmetry have chiral icosahedral symmetry:

Four Catalan solids, convex:

Triakis octahedron - isosceles triangles
Tetrakis hexahedron - isosceles triangles
Deltoidal icositetrahedron - kites
Pentagonal icositetrahedron - pentagons

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

References

[edit]

^ "Greek numerical prefixes".

Weisstein, Eric W. "Icositetrahedron". 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 (16) semiregular polyhedron (two infinite groups and 50)
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

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