# Cuboctatruncated cuboctahedron

Cuboctatruncated cuboctahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymCotco
Coxeter diagramx4/3x3x4*a (   )
Elements
Faces8 hexagons, 6 octagons, 6 octagrams
Edges24+24+24
Vertices48
Vertex figureScalene triangle, edge lengths 3, 2+2, 2–2 Measures (edge length 1)
Circumradius$\frac{\sqrt7}{2} ≈ 1.32288$ Volume10
Dihedral angles8/3–6: $\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439^\circ$ 8/3–8: 90°
8–6: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ$ Central density4
Number of external pieces62
Level of complexity15
Related polytopes
ArmySemi-uniform Girco, edge lengths $\sqrt2-1$ (of octagons) and 1 (ditrigon-rectangle)
RegimentCotco
ConjugateCuboctatruncated cuboctahedron
Convex coreCube
Abstract & topological properties
Flag count288
Euler characteristic-4
OrientableYes
Genus3
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

The cuboctatruncated cuboctahedron or cotco, also called the cubitruncated cuboctahedron, is a uniform polyhedron. It consists of 8 hexagons, 6 octagons, and 6 octagrams, with one of each type of face meeting per vertex.

## Vertex coordinates

A cuboctatruncated cuboctahedron of edge length 1 has vertex coordinates given by all permutations of:

• $\left(±\frac{1+\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$ ## Related polyhedra

(degenerate, double cover of cube) x4/3o3o4*a (   )
Great cubicuboctahedron gocco x4/3x3o4*a (   )
(degenerate, oct+6(4)) o4/3x3o4*a (   )
(degenerate, double cover of cho) o4/3x3x4*a (   )
(degenerate, oct+6(4)) o4/3o3x4*a (   )
Small cubicuboctahedron socco x4/3o3x4*a (   )
Cuboctatruncated cuboctahedron cotco x4/3x3x4*a (   )