Tetrahedral prism
Jump to navigation
Jump to search
Tetrahedral prism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Tepe 
Coxeter diagram  x x3o3o () 
Tapertopic notation  1^{2}1 
Elements  
Cells  2 tetrahedra, 4 triangular prisms 
Faces  8 triangles, 6 squares 
Edges  4+12 
Vertices  8 
Vertex figure  Triangular pyramid, edge lengths 1 (base), √2 (legs) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Tet–3trip: 90° 
Trip–4–trip:  
Heights  Tet atop tet: 1 
Dyad atop trip:  
Square atop ortho square:  
Central density  1 
Number of external pieces  6 
Level of complexity  4 
Related polytopes  
Army  Tepe 
Regiment  Tepe 
Dual  Tetrahedral tegum 
Conjugate  None 
Abstract & topological properties  
Flag count  192 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  A_{3}×A_{1}, order 48 
Convex  Yes 
Nature  Tame 
The tetrahedral prism or tepe is a prismatic uniform polychoron that consists of 2 tetrahedra and 4 triangular prisms. Each vertex joins 1 tetrahedron and 3 triangular prisms. As the name suggests, it is a prism based on a tetrahedron, and as such is also a segmentochoron (designated K4.9 in Richard Klitzing's list).
Gallery[edit  edit source]

Segmentochoron display, tet atop tet

Segmentochoron display, square atop orthogonal square

Net

Card with cell counts, verf, and crosssections
Vertex coordinates[edit  edit source]
The vertices of a tetrahedral prism of edge length 1 are given by all even sign changes of the first three coordinates of:
 .
Representations[edit  edit source]
A tetrahedral prism has the following Coxeter diagrams:
 x x3o3o () (full symmetry)
 x2s4o3o () (prism of alternated cube)
 x2s2s4o () (prism of alternated square prism)
 x2s2s2s () (prism of alternated cuboid)
 xx3oo3oo&#x (bases considered separate)
 xx ox3oo&#x (A_{2}×A_{1} axial, dyad atop triangular prism)
 xx xo ox&#x (A_{1}×A_{1}×A_{1} axial, square atop orthogonal square)
 oox xxx&#x (base has one symmetry axis only)
 xxxx&#x (irregular bases)
 xxoo ooxx&#xr (A_{1}×A_{1} axial)
 oxxo3oooo&#xr (A_{2} axial)
External links[edit  edit source]
 Bowers, Jonathan. "Category 19: Prisms" (#889).
 Klitzing, Richard. "Tepe".
 Wikipedia contributors. "Tetrahedral prism".