Stellated cube

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Stellated cube
Rank3
TypeRegular
Notation
Schläfli symbol{4/2,4}
Elements
Components3 square hosohedra
Faces12 digons as 6 stellated squares
Edges12
Vertices6
Vertex figureSquare, edge length 0
Measures (edge length 1)
Circumradius
Volume0
Dihedral angle90°
Central density3
Related polytopes
ArmyOct
RegimentStellated cube
DualGreat cube
Abstract & topological properties
Schläfli type{2,4}
OrientableYes
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

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[edit | edit source]

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

  • .