# Great cube

Great cube
Rank3
TypeRegular
Notation
Schläfli symbol{4,4/2}
Elements
Components3 square dihedra
Faces6 squares
Edges12
Vertices6 doubled
Vertex figureStellated square, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Volume0
Dihedral angle
Central density3
Related polytopes
ArmyOct
RegimentOct
DualStellated cube
Abstract & topological properties
Schläfli type{4,2}
OrientableYes
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

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:

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