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{{Uniform polyhedra db|Uniform dual polyhedron stat table|ctCO}}
{{Uniform polyhedra db|Uniform dual polyhedron stat table|ctCO}}
[[File:Tetradyakis hexahedron.stl|thumb|3D model of a tetradyakis hexahedron]]
[[File:Tetradyakis hexahedron.stl|thumb|3D model of a tetradyakis hexahedron]]
The '''tetradyakis hexahedron''' (or '''great disdyakis dodecahedron''') is a nonconvex [[Isohedral figure|isohedral]] [[polyhedron]]. It has 48 intersecting [[scalene triangle]] faces, 72 edges, and 20 vertices.
The '''tetradyakis hexahedron''' (or '''great disdyakis dodecahedron''') is a nonconvex [[Isohedral figure|isohedral]] [[polyhedron]]. It has 48 intersecting [[scalene triangle]] faces, 72 edges, and 20 vertices. The triangles have one angle of <math>\arccos(\frac{3}{4})\approx 41.409\,622\,109\,27^{\circ}</math>, one of <math>\arccos(\frac{1}{6}+\frac{7}{12}\sqrt{2})\approx 7.420\,694\,647\,42^{\circ}</math> and one of <math>\arccos(\frac{1}{6}-\frac{7}{12}\sqrt{2})\approx 131.169\,683\,243\,31^{\circ}</math>. The [[dihedral angle]] equals <math>\arccos(-\frac{5}{7})\approx 135.584\,691\,402\,81^{\circ}</math>. Part of each triangle lies within the solid, hence is invisible in solid models.


It is the [[Dual polyhedron|dual]] of the [[uniform star polyhedron|uniform]] cubitruncated cuboctahedron.
It is the [[Dual polyhedron|dual]] of the [[uniform star polyhedron|uniform]] cubitruncated cuboctahedron.

== See also ==
== See also ==
* [[List of uniform polyhedra]]
* [[List of uniform polyhedra]]

Revision as of 13:53, 2 July 2020

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}
Coxeter diagram
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
3D model of a 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]

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))

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
3D model of a tetradyakis hexahedron

The tetradyakis hexahedron (or great disdyakis dodecahedron) is a nonconvex isohedral polyhedron. It has 48 intersecting scalene triangle faces, 72 edges, and 20 vertices. 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.

It is the dual of the uniform cubitruncated cuboctahedron.

See also

References

  1. ^ Maeder, Roman. "16: cubitruncated cuboctahedron". MathConsult.{{cite web}}: CS1 maint: url-status (link)