Dodecagonal tegum

Dodecagonal tegum
Rank	3
Type	Uniform dual
Space	Spherical
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	$\arccos\left(-\frac{15+8\sqrt3}{33}\right) \approx 150.97836^\circ$
Central density	1
Related polytopes
Army	Twit
Regiment	Twit
Dual	Dodecagonal prism
Conjugate	Dodecagrammic tegum
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	I2(12)×A1, order 48
Convex	Yes
Nature	Tame

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 $2\sqrt{26+15\sqrt3} \approx 14.41954$.