# Decagonal tegum

Decagonal tegum Rank3
TypeUniform dual
SpaceSpherical
Bowers style acronymDet
Info
Coxeter diagramm2m10o
SymmetryI2(10)×A1, order 40
ArmyDet
RegimentDet
Elements
Vertex figure2 decagons, 10 squares
Faces20 isosceles triangles
Edges10+20
Vertices2+10
Measures (edge length 1)
Dihedral angle$\arccos\left(-\frac{15+4\sqrt5}{29}\right) ≈ 145.65592°$ Central density1
Euler characteristic2
Related polytopes
DualDecagonal prism
ConjugateDecagrammic tegum
Properties
ConvexYes
OrientableYes
NatureTame

The decagonal tegum or det, also called a decagonal dipyramib, is a tegum with a decagon as the midsection, constructed as the dual of a decagonal prism. It has 20 isosceles triangles as faces, with 2 order–10 and 10 order–4 vertices. .

In the variant obtained as the dual of a uniform decagonal prism, the side edges are $3+\sqrt5 ≈ 5.23607$ times the length of the edges of the base decagon. Each face has apex angle $\arccos\left(3\frac{3+\sqrt5}{16}\right) ≈ 10.95922°$ and base angles $\arccos\left(\frac{3-\sqrt5}{8}\right) \approx 84.52039°$ . If the base decagon has edge length 1, its height is $\sqrt{50+22\sqrt5} ≈ 9.95959$ .