Tetragonal disphenoid

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Tetragonal disphenoid
Rank3
TypeNoble
SpaceSpherical
Bowers style acronymTedow
Info
Coxeter diagramxo ox&#y
SymmetryBC2×A1+, order 8
ArmyTedow
RegimentTedow
Elements
Vertex figureIsosceles triangle
Faces4 isosceles triangles
Edges2+4
Vertices4
Measures (edge lengths b [base], ℓ [lacing])
Circumradius
Height
Central density1
Euler characteristic2
Related polytopes
DualTetragonal disphenoid
ConjugateTetragonal disphenoid
Properties
ConvexYes
OrientableYes
NatureTame

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.