# Rhombic disphenoid

Rhombic disphenoid
Rank3
TypeNoble
SpaceSpherical
Bowers style acronymRhodow
Info
Coxeter diagrams2s2s
SymmetryA1×A1×A1+, order 4
ArmyRhodow
RegimentRhodow
Elements
Vertex figureScalene triangle
Faces4 scalene triangles
Edges2+2+2
Vertices4
Measures (edge lengths a, b, c)
Circumradius${\displaystyle \sqrt{\frac{a^2+b^2+c^2}{8}}}$
Central density1
Euler characteristic2
Related polytopes
DualRhombic disphenoid
ConjugateRhombic disphenoid
Properties
ConvexYes
OrientableYes
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, along with a number of other isogonal polychora.