Cubical bipyramid
From HandWiki
| 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
External links
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