Cuboctatruncated cuboctahedron

Cuboctatruncated cuboctahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Cotco
Coxeter diagram	x4/3x3x4*a ()
Elements
Faces	8 hexagons, 6 octagons, 6 octagrams
Edges	24+24+24
Vertices	48
Vertex figure	Scalene triangle, edge lengths √3, √2+√2, √2–√2
Measures (edge length 1)
Circumradius	$\frac{\sqrt7}{2} ≈ 1.32288$
Volume	10
Dihedral angles	8/3–6: $\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439^\circ$
	8/3–8: 90°
	8–6: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ$
Central density	4
Number of external pieces	62
Level of complexity	15
Related polytopes
Army	Semi-uniform Girco, edge lengths $\sqrt2-1$ (of octagons) and 1 (ditrigon-rectangle)
Regiment	Cotco
Dual	Tetradyakis hexahedron
Conjugate	Cuboctatruncated cuboctahedron
Convex core	Cube
Abstract & topological properties
Flag count	288
Euler characteristic	-4
Orientable	Yes
Genus	3
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

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

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

• Bowers, Jonathan. "Polyhedron Category 5: Omnitruncates" (#62).

• Klitzing, Richard. "cotco".

• Wikipedia Contributors. "Cubitruncated cuboctahedron".
• McCooey, David. "Cubitruncated Cuboctahedron"