Dodecagonal triotegum

Dodecagonal triotegum
File:Dodecagonal triotegum.png (OFF file)
Rank	6
Type	Noble
Notation
Bowers style acronym	Twattit
Coxeter diagram	m12o2m12o2m12o
Elements
Peta	1728 digonal trisphenoids
Tera	5184 tetragonal disphenoidal pyramids
Cells	5184 digonal disphenoids, 432 tetragonal disphenoids
Faces	864 isosceles triangles, 1728 triangles
Edges	36+432
Vertices	36
Vertex figure	Dodecagonal duotegmatic tegum
Measures (based on dodecagons of edge length 1)
Edge lengths	Base (36): 1
	Lacing (432): $1+{\sqrt {3}}\approx 2.73205$
Circumradius	${\frac {{\sqrt {2}}+{\sqrt {6}}}{2}}\approx 1.93185$
Inradius	${\frac {3+2{\sqrt {3}}}{6}}\approx 1.07735$
Central density	1
Related polytopes
Army	Twattit
Regiment	Twattit
Dual	Dodecagonal trioprism
Conjugate	Dodecagrammic triotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(12)≀S3, order 82944
Convex	Yes
Nature	Tame

The dodecagonal triotegum or twattit is a noble triotegum that consists of 1728 digonal trisphenoids and 36 vertices. 288 facets join at each vertex. It is also the 36-11-13 step prism.