Cubitruncated cuboctahedron

Template:Short description Template:Uniform polyhedra db File:Cubitruncated cuboctahedron.stl 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, and has a shäfli symbol of tr{4,³/₂}

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

(±(Template:Radic−1), ±1, ±(Template:Radic+1))

Related polyhedra

Tetradyakis hexahedron

Template:Uniform polyhedra db File:Tetradyakis hexahedron.stl 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 $\arccos (\frac{3}{4})\approx 41.40962210927^{\circ }$, one of $\arccos (\frac{1}{6}+\frac{7}{12}\sqrt{2})\approx 7.42069464742^{\circ }$ and one of $\arccos (\frac{1}{6}-\frac{7}{12}\sqrt{2})\approx 131.16968324331^{\circ }$. The dihedral angle equals $\arccos (-\frac{5}{7})\approx 135.58469140281^{\circ }$. 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

• List of uniform polyhedra

References

• Template:Citation p. 92

External links

• Template:Mathworld
• Template:Mathworld
• http://gratrix.net Uniform polyhedra and duals

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