Tetrahedral prism

From Polytope Wiki
Jump to navigation Jump to search
Tetrahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymTepe
Coxeter diagramx x3o3o ()
Tapertopic notation121
Elements
Cells2 tetrahedra, 4 triangular prisms
Faces8 triangles, 6 squares
Edges4+12
Vertices8
Vertex figureTriangular pyramid, edge lengths 1 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTet–3-trip: 90°
 Trip–4–trip:
HeightsTet atop tet: 1
 Dyad atop trip:
 Square atop ortho square:
Central density1
Number of external pieces6
Level of complexity4
Related polytopes
ArmyTepe
RegimentTepe
DualTetrahedral tegum
ConjugateNone
Abstract & topological properties
Flag count192
Euler characteristic0
OrientableYes
Properties
SymmetryA3×A1, order 48
ConvexYes
NatureTame

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 K-4.9 in Richard Klitzing's list).

Gallery[edit | edit source]

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 (A2×A1 axial, dyad atop triangular prism)
  • xx xo ox&#x (A1×A1×A1 axial, square atop orthogonal square)
  • oox xxx&#x (base has one symmetry axis only)
  • xxxx&#x (irregular bases)
  • xxoo ooxx&#xr (A1×A1 axial)
  • oxxo3oooo&#xr (A2 axial)

External links[edit | edit source]