Cubic pyramid

Cubic pyramid
Schlegel diagram
Type	Polyhedral pyramid
Schläfli symbols	( ) ∨ {4,3} ( ) ∨ [{4} × { }] ( ) ∨ [{ } × { } × { }]
Cells	7	1 {4,3} 6 ( ) ∨ {4}
Faces	18	12 {3} 6 {4}
Edges	20
Vertices	9
Dual	Octahedral pyramid
Symmetry group	B3, [4,3,1], order 48 [4,2,1], order 16 [2,2,1], order 8
Properties	convex, regular-faced

In 4-dimensional geometry, the cubic pyramid is bounded by one cube on the base and 6 square pyramid cells which meet at the apex. Since a cube has a circumradius divided by edge length less than one, the square pyramids can made with regular faces by computing the appropriate height.

The regular 24-cell has cubic pyramids around every vertex.

The dual to the cubic pyramid is a octahedral pyramid, seen as an octahedral base, and 8 regular tetrahedral meeting at an apex.

Related polytopes and honeycombs

A cubic pyramid of height zero can be seen as a cube divided into 6 square pyramids along with the center point. These square pyramid-filled cubes can tessellate three-dimensional space as a dual of the truncated cubic honeycomb, called a hexakis cubic honeycomb, or pyramidille.

External links

• Olshevsky, George, Pyramid at Glossary for Hyperspace.
• Richard Klitzing, 4D, Segmentotopes Richard Klitzing, Segmentotope, cubpy, K-4.26
• Richard Klitzing, Axial-Symmetrical Edge Facetings of Uniform Polyhedra