# Dodecahedral tegum

Dodecahedral tegum
Rank4
TypeUniform dual
SpaceSpherical
Notation
Bowers style acronymDote
Coxeter diagramm2o3o5m
Elements
Cells24 pentagonal pyramids
Faces60 isosceles triangles, 12 pentagons
Edges30+40
Vertices2+20
Vertex figure2 dodecahedra, 20 triangular tegums
Measures (edge length 1)
Central density1
Related polytopes
Army'Dote
RegimentDote
DualIcosahedral prism
ConjugateGreat stellated dodecahedral tegum
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexYes
NatureTame

The dodecahedral tegum or dote, also called the dodecahedral bipyramid, is a convex isochoric polychoron with 24 pentagonal pyramids as cells. As the name suggests, it can be constructed as a tegum based on the dodecahedron.

It is the only tegum based on a Platonic solid that can't be made CRF.

In the variant obtained as the dual of the uniform icosahedral prism, the height from the top to the bottom vertex is ${\displaystyle 2+\sqrt5 ≈ 4.23607}$ times the edge length of the base dodecahedron.