# Dodecagonal tegum

Dodecagonal tegum Rank3
TypeUniform dual
SpaceSpherical
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$\arccos\left(-\frac{15+8\sqrt3}{33}\right) \approx 150.97836^\circ$ Central density1
Related polytopes
ArmyTwit
RegimentTwit
DualDodecagonal prism
ConjugateDodecagrammic tegum
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryI2(12)×A1, order 48
ConvexYes
NatureTame

The dodecagonal tegum or twit, 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 $4+2\sqrt3 \approx 7.46410$ times the length of the edges of the base dodecagon. Each face has apex angle $\arccos\left(\frac{1+4\sqrt3}{8}\right) \approx 7.68193^\circ$ and base angles $\arccos\left(\frac{2-\sqrt3}{4}\right) \approx 86.15903^\circ$ . If the base dodecagon has edge length 1, its height is $2\sqrt{26+15\sqrt3} \approx 14.41954$ .