Tetrahedral tegum
Tetrahedral tegum  

Rank  4 
Type  CRF 
Notation  
Bowers style acronym  Tete 
Coxeter diagram  oxo3ooo3ooo&#xt 
Elements  
Cells  8 tetrahedra 
Faces  4+12 triangles 
Edges  6+8 
Vertices  2+4 
Vertex figure 

Measures (edge length 1)  
Inradius  
Hypervolume  
Dichoral angles  Tet–3–tet equatorial: 
Tet–3–tet pyramidal:  
Height  
Central density  1 
Related polytopes  
Army  Tete 
Regiment  Tete 
Dual  Semiuniform tetrahedral prism 
Conjugate  None 
Abstract & topological properties  
Flag count  192 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  A_{3}×A_{1}, order 48 
Flag orbits  4 
Convex  Yes 
Nature  Tame 
The tetrahedral tegum, also called the tetrahedral bipyramid, is a CRF polychoron with 8 identical regular tetrahedra as cells. As such it is also a Blind polytope. As the name suggests, it is a tegum based on the tetrahedron, formed by attaching two regular pentachora at a common cell.
Vertex coordinates[edit  edit source]
The vertices of a tetrahedral tegum of edge length 1 are given by:
 ,
 ,
 ,
 .
Representations[edit  edit source]
A tetrahedral tegum has the following Coxeter diagrams:
 oxo3ooo3ooo&#xt
 yo ox3oo3oo&#xt (y = , as full tegum)
 oyo oox3ooo&#xt (as triangular pyramidal tegum)
Variations[edit  edit source]
The tetrahedral tegum can have the heights of its pyramids varied while maintaining its full symmetry These variants generally have 8 nonCRF triangular pyramids as cells.
One notable variation can be obtained as the dual of the uniform tetrahedral prism, which can be represented by m2m3o3o (). In this variation the height between the top and bottom vertices of the tegum is exactly times the length of the edges of the base tetrahedron, and all the dichoral angles are .
External links[edit  edit source]
 Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
 Klitzing, Richard. "tete".