# Dodecagonal duotegum

Dodecagonal duotegum
Rank4
TypeNoble
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): ${\displaystyle 1+{\sqrt {3}}\approx 2.73205}$
Circumradius${\displaystyle {\frac {{\sqrt {2}}+{\sqrt {6}}}{2}}\approx 1.93185}$
Inradius${\displaystyle {\frac {2{\sqrt {2}}+{\sqrt {6}}}{4}}\approx 1.31948}$
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:

• ${\displaystyle \left(\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,0,\,0\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,0,\,0\right),}$
• ${\displaystyle \left(\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right),}$
• ${\displaystyle \left(0,\,0,\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}}\right),}$
• ${\displaystyle \left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}}\right),}$
• ${\displaystyle \left(0,\,0,\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right).}$