Dodecagonal tegum

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.

Dodecagonal tegum
Rank	3
Type	Uniform dual
Notation
Bowers style acronym	Twit
Coxeter diagram	m2m12o
Elements
Faces	24 isosceles triangles
Edges	12+24
Vertices	2+12
Vertex figure	2 dodecagons, 12 squares
Measures (edge length 1)
Dihedral angle	$\arccos \left(-{\frac {15+8{\sqrt {3}}}{33}}\right)\approx 150.97836^{\circ }$
Central density	1
Number of external pieces	24
Level of complexity	3
Related polytopes
Army	Twit
Regiment	Twit
Dual	Dodecagonal prism
Conjugate	Dodecagrammic tegum
Abstract & topological properties
Flag count	144
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	I2(12)×A1, order 48
Convex	Yes
Nature	Tame

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