Irregular tetrahedron

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Irregular tetrahedron
Rank3
Notation
Bowers style acronymIrtet
Coxeter diagramoooo&#x
Elements
Faces1+1+1+1 scalene triangles
Edges1+1+1+1+1+1
Vertices1+1+1+1
Vertex figure1+1+1+1 scalene triangles
Measures (edge length 1)
Central density1
Related polytopes
ArmyIrtet
RegimentIrtet
DualIrregular tetrahedron
ConjugateIrregular tetrahedron
Abstract & topological properties
Flag count24
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryI×I×I, order 1
Flag orbits24
ConvexYes
NatureTame

An irregular tetrahedron is a tetrahedron with no symmetries. Generally, though not necessarily, it has four different scalene triangles for faces.

In vertex figures[edit | edit source]

A total of 17 uniform polychora, including the convex great disprismatotesseractihexadecachoron and great disprismatohexacosihecatonicosachoron, have irregular tetrahedra for vertex figures. These are known as omnitruncates or maximized polychora and have the most vertices possible to be uniform in their symmetry.