Great truncated cuboctahedron
Great truncated cuboctahedron | |
---|---|
Type | Uniform star polyhedron |
Elements | F = 26, E = 72 V = 48 (χ = 2) |
Faces by sides | 12{4}+8{6}+6{8/3} |
Wythoff symbol | 2 3 4/3 | |
Symmetry group | Oh, [4,3], *432 |
Index references | U20, C67, W93 |
Dual polyhedron | Great disdyakis dodecahedron |
Vertex figure | 4.6/5.8/3 |
Bowers acronym | Quitco |
File:Great truncated cuboctahedron.stl In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron or stellatruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed as U20. It has 26 faces (12 squares, 8 hexagons and 6 octagrams), 72 edges, and 48 vertices.[1] It is represented by the Schläfli symbol tr{4/3,3}, and Coxeter-Dynkin diagram . It is sometimes called the quasitruncated cuboctahedron because it is related to the truncated cuboctahedron, , except that the octagonal faces are replaced by {8/3} octagrams.
Convex hull
Its convex hull is a nonuniform truncated cuboctahedron. The truncated cuboctahedron and the great truncated cuboctahedron form isomorphic graphs despite their different geometric structure.
Orthographic projections
Cartesian coordinates
Cartesian coordinates for the vertices of a great truncated cuboctahedron centered at the origin are all permutations of [math]\displaystyle{ \Bigl( \pm 1, \ \pm\left[1-\sqrt 2 \right], \ \pm\left[1-2\sqrt 2\right]\Bigr). }[/math]
See also
References
External links
- Weisstein, Eric W.. "Great truncated cuboctahedron". http://mathworld.wolfram.com/GreatTruncatedCuboctahedron.html.
Original source: https://en.wikipedia.org/wiki/Great truncated cuboctahedron.
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