# Decagonal duotegum

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.

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): $\frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825$ Circumradius$\frac{1+\sqrt5}{2} ≈ 1.61803$ Inradius$\sqrt{\frac{5+2\sqrt5}{8}} ≈ 1.08813$ Central density1
Euler characteristic0
Related polytopes
DualDecagonal duoprism
ConjugateDecagrammic duotegum
Properties
ConvexYes
OrientableYes
NatureTame

## Vertex coordinates

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

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