Cubic bipyramid

Orthographic projection
8 red vertices and 12 blue edges of central cube, with 2 yellow apex vertices.
Type Polyhedral bipyramid
Schläfli symbol {4,3} + { }
dt{2,3,4}
Coxeter-Dynkin
Cells 12 {4}∨{ } (2×6)
Faces 30 triangles (2×12+6)
Edges 28 (2×8+12)
Vertices 10 (2+8)
Dual Octahedral prism
Symmetry group [2,4,3], order 96
Properties convex, regular-faced,CRF polytope, Hanner polytope

In 4-dimensional geometry, the cubical bipyramid is the direct sum of a cube and a segment, {4,3} + { }. Each face of a central cube is attached with two square pyramids, creating 12 square pyramidal cells, 30 triangular faces, 28 edges, and 10 vertices. A cubical bipyramid can be seen as two cubic pyramids augmented together at their base.[1]

It is the dual of a octahedral prism.

Being convex and regular-faced, it is a CRF polytope.

Coordinates

It is a Hanner polytope with coordinates:[2]

  • [2] (0, 0, 0; ±1)
  • [8] (±1, ±1, ±1; 0)

See also

References

  1. "Cute".
  2. "Hanner polytopes".
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