# Dodecagonal tegum

Dodecagonal tegum
Rank3
TypeUniform dual
SpaceSpherical
Bowers style acronymTwit
Info
Coxeter diagramm2m12o
SymmetryI2(12)×A1, order 48
ArmyTwit
RegimentTwit
Elements
Vertex figure2 dodecagons, 12 squares
Faces24 isosceles triangles
Edges12+24
Vertices2+12
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos\left(-\frac{15+8\sqrt3}{33}\right) ≈ 150.97836°}$
Central density1
Euler characteristic2
Related polytopes
DualDodecagonal prism
ConjugateDodecagrammic tegum
Properties
ConvexYes
OrientableYes
NatureTame

The dodecagonal tegum or twit, also called a dodecagonal dipyramib, 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 ${\displaystyle 4+2\sqrt3 ≈ 7.46410}$ times the length of the edges of the base dodecagon. Each face has apex angle ${\displaystyle \arccos\left(\frac{1+4\sqrt3}{8}\right) \approx 7.68193°}$ and base angles ${\displaystyle \arccos\left(\frac{2-\sqrt3}{4}\right) \approx 86.15903°}$. If the base dodecagon has edge length 1, its height is ${\displaystyle \sqrt{10+6\sqrt3} ≈ 14.41954}$.