Cubic pyramid

Cubic pyramid

Schlegel diagram
Type Polyhedral pyramid
Schläfli symbol ( ) ∨ {4,3}
( ) ∨ [{4} × { }]
( ) ∨ [{ } × { } × { }]
Cells 7 1 cube
6 square pyramids
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,[1] 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.

References

  1. Richard Klitzing, 3D convex uniform polyhedra, o3o4x - cube sqrt(3)/2 = 0.866025

External links

Wikimedia Commons has media related to Pyramids (geometry).