# Decagonal duotegum

Decagonal duotegum
Rank4
TypeNoble
SpaceSpherical
Bowers style acronymDedit
Info
Coxeter diagramm10o2m10o
SymmetryI2(10)≀S2, order 800
ArmyDedit
RegimentDedit
Elements
Vertex figureDecagonal tegum
Cells100 tetragonal disphenoids
Faces200 isosceles triangles
Edges20+100
Vertices20
Measures (based on decagons of edge length 1)
Edge lengthsBase (20): 1
Lacing (100): ${\displaystyle \frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825}$
Circumradius${\displaystyle \frac{1+\sqrt5}{2} ≈ 1.61803}$
Inradius${\displaystyle \sqrt{\frac{5+2\sqrt5}{8}} ≈ 1.08813}$
Central density1
Euler characteristic0
Related polytopes
DualDecagonal duoprism
ConjugateDecagrammic duotegum
Properties
ConvexYes
OrientableYes
NatureTame

The decagonal duotegum or dedit, also known as the decagonal-decagonal duotegum, the 10 duotegum, or the 10-10 duotegum, is a noble duotegum that consists of 100 tetragonal disphenoids and 20 vertices, with 20 cells joining at each vertex. It is also the 20-9 step prism. It is the first in an infinite family of isogonal decagonal hosohedral swirlchora and also the first in an infinite family of isochoric decagonal dihedral swirlchora.

## Vertex coordinates

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

• ${\displaystyle \left(±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,0,\,0\right),}$
• ${\displaystyle \left(±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}},\,0,\,0\right),}$
• ${\displaystyle \left(±\frac{1+\sqrt5}{2},\,0,\,0,\,0\right),}$
• ${\displaystyle \left(0,\,0,\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2}\right),}$
• ${\displaystyle \left(0,\,0,\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}}\right),}$
• ${\displaystyle \left(0,\,0,\,±\frac{1+\sqrt5}{2},\,0\right).}$