Cubic tegum
The cubic tegum, also called the cubic bipyramid, is a CRF polychoron with 12 square pyramids as cells. As the name suggests, it is a tegum based on the cube, formed by attaching 2 cubic pyramids together at their common base. It is unique among CRF tegums as the height from the top to the bottom vertex is identical to the cube's edge length.
Cubic tegum  

Rank  4 
Type  CRF 
Notation  
Bowers style acronym  Cute 
Coxeter diagram  oxo4ooo3ooo&#xt 
Bracket notation  <[III]I> 
Elements  
Cells  12 square pyramids 
Faces  24 triangles, 6 squares 
Edges  12+16 
Vertices  2+8 
Vertex figures  2 cubes, edge length 1 
8 skewed triangular tegums, based edge length √2, side edge length 1  
Measures (edge length 1)  
Inradius  
Hypervolume  
Dichoral angles  Squippy–3–squippy: 120° 
Squippy–4–squippy: 90°  
Height  1 
Central density  1 
Related polytopes  
Dual  Semiuniform octahedral prism 
Conjugate  None 
Convex hull  Cubic tegum 
Abstract & topological properties  
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  B_{3}×A_{1}, order 96 
Convex  Yes 
Nature  Tame 
A regular icositetrachoron can be decomposed into 8 CRF cubic tegums sharing one common vertex.
Gallery edit

Wireframe, cell, net
Vertex coordinates edit
Coordinates for the vertices of a cubic tegum of edge length 1 are given by:
Representations edit
A cubic tegum has the following Coxeter diagrams:
 oxo4ooo3ooo&#xt (full symmetry)
 oxo oxo4ooo&#xt (square prismatic tegum)
 oxo oxo oxo&#xt (cuboid tegum)
 xo ox4oo3oo&#zx
 oxo xox4ooo&#xt (squarefirst)
 oxo xox xox&#xt (as above with rectangular symmetry)
Variations edit
The cubic tegum can have the heights of its pyramids varied while maintaining its full symmetry. These variants generally have 12 nonCRF square pyramids as cells.
One notable variation can be obtained as the dual of the uniform octahedral prism, which can be represented by m2o4o3m. In this variation the height between the top and bottom vertices of the tegum is times the length of the edges of the base cube, and all the dichoral angles are .
External links edit
 Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
 Klitzing, Richard. "cute".
 Hi.gher.Space Wiki Contributors. "Cubic bipyramid".