Since a cube has a circumradius divided by edge length less than one,[1] the square pyramids can be made with regular faces by computing the appropriate height.

This construction yields a tesseract with 8 cubical bounding cells, surrounding a central vertex with 16 edge-length long radii.

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

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.

The cubic pyramid can be folded from a three-dimensional net in the form of a non-convex tetrakis hexahedron, obtained by gluing square pyramids onto the faces of a cube, and folded along the squares where the pyramids meet the cube.