Great cube

Great cube
Rank	3
Type	Regular
Space	Spherical
Notation
Schläfli symbol	{4, 4/2}
Elements
Components	3 square dihedra
Faces	6 squares
Edges	12
Vertices	6 doubled
Vertex figure	Stellated square, edge length √2
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}2 \approx 0.70711$
Volume	0
Dihedral angle	0°
Central density	3
Related polytopes
Army	Oct
Regiment	Oct
Dual	Stellated cube
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

The great cube or compound of three square dihedra is a degenerate regular polyhedron compound, being the compound of three square dihedra. It has 6 square faces and 6 fissary vertices.

It can be formed as a degenerate stellation of the cube, by extending the faces to infinity.

When embedded in Euclidean 3-space all 6 of its faces pass through the center of the polyhedron.

Vertex coordinates

Coordinates for the vertices of a great cube of edge length 1 centered at the origin are given by all permutations of:

• $\left(\pm\frac{\sqrt2}{2},\,0,\,0\right)$.