|Bowers style acronym||Tedow|
|Coxeter diagram||xo ox&#y|
|Symmetry||BC2×A1+, order 8|
|Vertex figure||Isosceles triangle|
|Faces||4 isosceles triangles|
|Measures (edge lengths b [base], ℓ [lacing])|
The tetragonal disphenoid or tedow is a type of tetrahedron with four identical isosceles triangles for faces. It can also be considered a digonal antiprism. Tetragonal disphenoids, being digonal antiprisms, are related to rhombic disphenoids, which are digonal gyroprisms.
The general tetragonal disphenoid can be obtained as the alternation of a square prism. If the tetragonal disphenoid's base edges are of length b and its side edges are of length l, the corresponding square prism has base edge length and side edge length .
Vertex coordinates[edit | edit source]
The vertices of a tetragonal disphenoid with base edges of length b and side edges of length l are given by all even permutations of:
In vertex figures[edit | edit source]
Tetragonal disphenoids occur as vertex figures in 3 noble uniform polychora: the decachoron, the tetracontoctachoron, and the great tetracontoctachoron. They also appear as the vertex figure of any duoprism of two identical polygons.