Jump to content

Cubitruncated cuboctahedron

From Wikipedia, the free encyclopedia
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] and has a shäfli symbol of tr{4,3/2}

Convex hull

[edit]

Its convex hull is a nonuniform truncated cuboctahedron.


Convex hull

Cubitruncated cuboctahedron

Orthogonal projection

[edit]

Cartesian coordinates

[edit]

Cartesian coordinates for the vertices of a cubitruncated cuboctahedron are all the permutations of

(±(2−1), ±1, ±(2+1))
[edit]

Tetradyakis hexahedron

[edit]
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.

Proportions

[edit]

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

[edit]

References

[edit]
  1. ^ Maeder, Roman. "16: cubitruncated cuboctahedron". MathConsult. Archived from the original on 2015-03-29.
[edit]