Octahedral pyramid
| Octahedral pyramid | |
|---|---|
| Type | Polyhedral pyramid |
| Schläfli symbol | ( ) ∨ {3,4} ( ) ∨ r{3,3} ( ) ∨ s{2,6} ( ) ∨ [{4} + { }] ( ) ∨ [{ } + { } + { }] |
| Cells | 1 {3,4} 8 ( ) ∨ {3} |
| Faces | 20 {3} |
| Edges | 18 |
| Vertices | 7 |
| Symmetry group | B3, [4,3,1], order 48 [3,3,1], order 24 [2+,6,1], order 12 [4,2,1], order 16 [2,2,1], order 8 |
| Dual | Cubic pyramid |
| Properties | convex, regular-cells, Blind polytope |
In 4-dimensional geometry, the octahedral pyramid is bounded by one octahedron on the base and 8 triangular pyramid cells which meet at the apex. Since an octahedron has a circumradius divided by edge length less than one, the triangular pyramids can be made with regular faces (as regular tetrahedrons) by computing the appropriate height.
Having all regular cells, it is a Blind polytope. Two copies can be augmented to make an octahedral bipyramid which is also a Blind polytope.