Rhombic disphenoid

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Rhombic disphenoid
Rank3
TypeNoble
Notation
Bowers style acronymRhodow
Coxeter diagrams2s2s ()
Elements
Faces4 scalene triangles
Edges2+2+2
Vertices4
Vertex figureScalene triangle
Measures (edge lengths a , b , c )
Circumradius
Central density1
Related polytopes
ArmyRhodow
RegimentRhodow
DualRhombic disphenoid
ConjugateRhombic disphenoid
Abstract & topological properties
Flag count24
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryK3+, order 4
Flag orbits6
ConvexYes
NatureTame

A rhombic disphenoid is a type of tetrahedron with 4 identical scalene triangles as faces. Rhombic disphenoids are related to tetragonal disphenoids, and can be considered to be the digonal version of gyroprisms.

A rhombic disphenoid can generally be formed by alternating a cuboid.

Rhombic disphenoids occur as cells in any n -d  step prism where both n  and d  are even, or if n  is even and d2 ≡ 1 mod n and is a divisor of 2n.