Cubitruncated cuboctahedron
In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U16. It has 20 faces (8 hexagons, 6 octagons, and 6 octagrams), 72 edges, and 48 vertices.[1]
Cubitruncated cuboctahedron | |
---|---|
Type | Uniform star polyhedron |
Elements | F = 20, E = 72 V = 48 (χ = −4) |
Faces by sides | 8{6}+6{8}+6{8/3} |
Wythoff symbol | 3 4 4/3 | |
Symmetry group | Oh, [4,3], *432 |
Index references | U16, C52, W79 |
Dual polyhedron | Tetradyakis hexahedron |
Vertex figure | 6.8.8/3 |
Bowers acronym | Cotco |
Convex hull
Its convex hull is a nonuniform truncated cuboctahedron.
Convex hull |
Cubitruncated cuboctahedron |
Orthogonal projection
Cartesian coordinates
Cartesian coordinates for the vertices of a cubitruncated cuboctahedron are all the permutations of
- (±(√2−1), ±1, ±(√2+1))
Related polyhedra
Tetradyakis hexahedron
Tetradyakis hexahedron | |
---|---|
Type | Star polyhedron |
Face | |
Elements | F = 48, E = 72 V = 20 (χ = −4) |
Symmetry group | Oh, [4,3], *432 |
Index references | DU16 |
dual polyhedron | Cubitruncated cuboctahedron |
The tetradyakis hexahedron (or great disdyakis dodecahedron) is a nonconvex isohedral polyhedron. It has 48 intersecting scalene triangle faces, 72 edges, and 20 vertices.
Proportions
The triangles have one angle of , one of and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models.
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gollark: The owners of``` code | type | clicks | uniqueViews | views | hoursRemaining | sick | createdAt | updatedAt -------+-----------+--------+-------------+-------+----------------+------+----------------------------+---------------------------- XAn** | hatchling | 8 | 842 | 9208 | 155 | t | 2018-09-04 17:51:17.146+00 | 2018-09-05 12:27:43.868+00 5eA** | hatchling | 17 | 571 | 6372 | 159 | t | 2018-09-05 02:07:02.204+00 | 2018-09-05 12:27:44.481+00 aLv** | hatchling | 1 | 1347 | 14052 | 109 | t | 2018-09-04 20:24:56.434+00 | 2018-09-05 12:27:44.483+00 wOv** | hatchling | 2 | 597 | 7407 | 153 | t | 2018-09-04 20:33:48.953+00 | 2018-09-05 12:27:44.483+00 dDW** | hatchling | 3 | 819 | 9280 | 157 | t | 2018-09-04 20:14:24.368+00 | 2018-09-05 12:27:44.482+00```should probably fog their stuff - they're autoexcluded from my hatchery, but not others.
gollark: That could be a cool hatchery/fansite feature.
gollark: Okay, so apparently that dropped it down to 87 dragons.
gollark: I've decided to just check whether the score is significantly (maybe 1.5x) bigger than the optimal score for their time.
See also
References
- Maeder, Roman. "16: cubitruncated cuboctahedron". MathConsult.
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208 p. 92
External links
- Weisstein, Eric W. "Cubitruncated cuboctahedron". MathWorld.
- Weisstein, Eric W. "Tetradyakis hexahedron". MathWorld.
- http://gratrix.net Uniform polyhedra and duals
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