Stellated cube

Stellated cube
Rank	3
Type	Regular
Space	Spherical
Notation
Schläfli symbol	{4/2,4}
Elements
Components	3 square hosohedra
Faces	12 digons as 6 stellated squares
Edges	12
Vertices	6
Vertex figure	Square, edge length 0
Measures (edge length 1)
Circumradius	$\frac12 = 0.5$
Volume	0
Dihedral angle	90°
Central density	3
Related polytopes
Army	Oct
Regiment	Stellated cube
Dual	Great cube
Abstract & topological properties
Schläfli type	{2,4}
Orientable	Yes
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

This article is about the degenerate regular polyhedron compound. For the isohedral deltahedron sometimes called the "stellated cube", see Augmented cube.

The stellated cube or compound of three square hosohedra is a degenerate regular polyhedron compound, being the compound of three square hosohedra. It has 12 digonal faces that form 6 stellated squares due to pairs falling in the same plane.

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

Its quotient prismatic equivalent is the hexateron, which is five-dimensional.

Vertex coordinates

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

• $\left(\pm\frac12,\,0,\,0\right)$.