# Dodecagonal tegum

Dodecagonal tegum
Rank3
TypeUniform dual
Notation
Bowers style acronymTwit
Coxeter diagramm2m12o
Elements
Faces24 isosceles triangles
Edges12+24
Vertices2+12
Vertex figure2 dodecagons, 12 squares
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left(-{\frac {15+8{\sqrt {3}}}{33}}\right)\approx 150.97836^{\circ }}$
Central density1
Number of external pieces24
Level of complexity3
Related polytopes
ArmyTwit
RegimentTwit
DualDodecagonal prism
ConjugateDodecagrammic tegum
Abstract & topological properties
Flag count144
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryI2(12)×A1, order 48
ConvexYes
NatureTame

The dodecagonal tegum, also called a dodecagonal bipyramid, is a tegum with a dodecagon as the midsection, constructed as the dual of a dodecagonal prism. It has 24 isosceles triangles as faces, with 2 order–12 and 12 order–4 vertices.

In the variant obtained as the dual of a uniform dodecagonal prism, the side edges are ${\displaystyle 4+2{\sqrt {3}}\approx 7.46410}$ times the length of the edges of the base dodecagon. Each face has apex angle ${\displaystyle \arccos \left({\frac {1+4{\sqrt {3}}}{8}}\right)\approx 7.68193^{\circ }}$ and base angles ${\displaystyle \arccos \left({\frac {2-{\sqrt {3}}}{4}}\right)\approx 86.15903^{\circ }}$. If the base dodecagon has edge length 1, its height is ${\displaystyle 2{\sqrt {26+15{\sqrt {3}}}}\approx 14.41954}$.