# Dodecagonal duotegum

Dodecagonal duotegum
Rank4
TypeNoble
SpaceSpherical
Notation
Coxeter diagramm12o2m12o
Elements
Cells144 tetragonal disphenoids
Faces288 isosceles triangles
Edges24+144
Vertices24
Vertex figureDodecagonal tegum
Measures (based on dodecagons of edge length 1)
Edge lengthsBase (24): 1
Lacing (144): $1+\sqrt3 ≈ 2.73205$ Circumradius$\frac{\sqrt2+\sqrt6}{2} ≈ 1.93185$ Inradius$\frac{2\sqrt2+\sqrt6}{4} ≈ 1.31948$ Central density1
Related polytopes
DualDodecagonal duoprism
ConjugateDodecagrammic duotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(12)≀S2, order 1152
ConvexYes
NatureTame

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:

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