Cubitruncated cuboctahedron

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Cubitruncated cuboctahedron
Cubitruncated cuboctahedron.png
Type Uniform star polyhedron
Elements F = 20, E = 72
V = 48 (χ = 4)
Faces by sides8{6}+6{8}+6{8/3}
Wythoff symbol 3 4 4/3 |
Symmetry group Oh, [4,3], *432
Index references U 16, C 52, W 79
Dual polyhedron Tetradyakis hexahedron
Vertex figure Cubitruncated cuboctahedron vertfig.png
6.8.8/3
Bowers acronym Cotco
3D model of a cubitruncated cuboctahedron Cubitruncated cuboctahedron.stl
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}

Contents

Convex hull

Its convex hull is a nonuniform truncated cuboctahedron.

Cubitruncated cuboctahedron convex hull.png
Convex hull
Cubitruncated cuboctahedron.png
Cubitruncated cuboctahedron

Orthogonal projection

Cubitruncated cuboctahedron ortho wireframes.png

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
DU16 tetradyakishexahedron.png
Type Star polyhedron
Face DU16 facets.png
Elements F = 48, E = 72
V = 20 (χ = 4)
Symmetry group Oh, [4,3], *432
Index references DU 16
dual polyhedron Cubitruncated cuboctahedron
3D model of a tetradyakis hexahedron Tetradyakis hexahedron.stl
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

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

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References

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