# Cuboctatruncated cuboctahedron

Cuboctatruncated cuboctahedron
Rank3
TypeUniform
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${\displaystyle {\frac {\sqrt {7}}{2}}\approx 1.32288}$
Volume10
Dihedral angles8/3–6: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
8/3–8: 90°
8–6: ${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Central density4
Number of external pieces62
Level of complexity15
Related polytopes
ArmySemi-uniform Girco, edge lengths ${\displaystyle {\sqrt {2}}-1}$ (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
Flag orbits6
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:

• ${\displaystyle \left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right).}$