Cuboctatruncated cuboctahedron

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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
Volume10
Dihedral angles8/3–6:
 8/3–8: 90°
 8–6:
Central density4
Number of external pieces62
Level of complexity15
Related polytopes
ArmySemi-uniform Girco, edge lengths (of octagons) and 1 (ditrigon-rectangle)
RegimentCotco
DualTetradyakis hexahedron
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[edit | edit source]

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

Related polyhedra[edit | edit source]

Oddly, it has the same circumradius as the rhombidodecadodecahedron.

o4/3o3o4*a truncations
Name OBSA CD diagram Picture
(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 ()


External links[edit | edit source]