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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.