# Compound of two cubes

Compound of two cubes
Rank3
TypeUniform
Notation
Coxeter diagramxo4ox xx
Elements
Components2 cubes
Faces8 squares, 4 squares as 2 stellated octagons
Edges8+16
Vertices16
Vertex figureEquilateral triangle, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Volume2
Dihedral angle90°
Height1
Central density2
Number of external pieces18
Level of complexity6
Related polytopes
ArmySemi-uniform Op, edge lengths ${\displaystyle {\sqrt {\frac {2-{\sqrt {2}}}{2}}}}$ (base), 1 (sides)
Regiment*
DualCompound of two octahedra
ConjugateCompound of two cubes
Abstract & topological properties
Flag count96
OrientableYes
Properties
SymmetryI2(8)×A1, order 32
ConvexNo
NatureTame

The stellated octagonal prism or compound of two cubes is a prismatic uniform polyhedron compound. It consists of 2 stellated octagons and 8 squares. Each vertex joins one stellated octagon and two squares. As the name suggests, it is a prism based on a stellated octagon.

Its quotient prismatic equivalent is the square antiprismatic prism, which is four-dimensional.

## Vertex coordinates

Coordinates for the vertices of a stellated octagonal prism of edge length 1 centered at the origin are given by:

• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{2}},\,0,\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(0,\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right).}$

## Variations

This compound has variants where the bases are non-regular compounds of two squares. In these cases the compound has only square prismatic symmetry and the convex hull is a ditetragonal prism.