Square tettene

Square tettene
Rank5
TypeConvex regular-faced
Notation
Bowers style acronymSquete
Elements
Tera
Cells
Faces1+12+12 triangles, 1 square
Edges3+4+12
Vertices3+4
Vertex figure4 triangular scalene, 3 square scalenes
Measures (edge length 1)
Central density1
Related polytopes
DualSquare tettene
Abstract & topological properties
Flag count960
Euler characteristic2
OrientableYes
Properties
SymmetryA3▲B3, order 48
Flag orbits20
ConvexYes
NatureTame

The square tettene (OBSA: squete) also known as the triangular-square disphenoid, is a convex CRF 5-polytope with 3 square scalenes and 4 pentachora as facets and 7 vertices. Along with the 5-simplex (considered as a triangular disphenoid), they are the only convex equilateral disphenoids in 5-dimensional space.

Vertex coordinates

The vertices of a square tettene with unit edge length are given by:

• ${\displaystyle \left(0,\,{\dfrac {\sqrt {3}}{3}},\,0,\,0,\,{\dfrac {\sqrt {6}}{12}}\right)}$,
• ${\displaystyle \left(\pm {\dfrac {1}{2}},\,-{\dfrac {\sqrt {3}}{6}},\,0,\,0,\,{\dfrac {\sqrt {6}}{12}}\right)}$,
• ${\displaystyle \left(0,\,0,\,\pm {\dfrac {1}{2}},\,\pm {\dfrac {1}{2}},\,-{\dfrac {\sqrt {6}}{12}}\right)}$.