Dodecagonal duotegum

Dodecagonal duotegum
(OFF file)
Rank	4
Type	Noble
Space	Spherical
Notation
Bowers style acronym	Twaddit
Coxeter diagram	m12o2m12o
Elements
Cells	144 tetragonal disphenoids
Faces	288 isosceles triangles
Edges	24+144
Vertices	24
Vertex figure	Dodecagonal tegum
Measures (based on dodecagons of edge length 1)
Edge lengths	Base (24): 1
	Lacing (144): $1+\sqrt3 ≈ 2.73205$
Circumradius	$\frac{\sqrt2+\sqrt6}{2} ≈ 1.93185$
Inradius	$\frac{2\sqrt2+\sqrt6}{4} ≈ 1.31948$
Central density	1
Related polytopes
Army	Twaddit
Regiment	Twaddit
Dual	Dodecagonal duoprism
Conjugate	Dodecagrammic duotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(12)≀S2, order 1152
Convex	Yes
Nature	Tame

The dodecagonal duotegum or twaddit, also known as the dodecagonal-dodecagonal duotegum, the 12 duotegum, or the 12-12 duotegum, is a noble duotegum that consists of 144 tetragonal disphenoids and 24 vertices, with 24 cells joining at each vertex. . It is also the 24-11 step prism. It is the first in an infinite family of isogonal dodecagonal hosohedral swirlchora and also the first in an infinite family of isochoric dodecagonal dihedral swirlchora.

Vertex coordinates

The vertices of a dodecagonal duotegum based on 2 dodecagons of edge length 1, centered at the origin, are given by:

• $\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,0,\,0\right),$
• $\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,0,\,0\right),$
• $\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,0,\,0\right),$
• $\left(0,\,0,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$
• $\left(0,\,0,\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$
• $\left(0,\,0,\,±\frac{2+\sqrt3}{2},\,±\frac12\right).$