# Decagonal antitegum

Decagonal antitegum
Rank3
TypeUniform dual
Notation
Bowers style acronymDat
Coxeter diagramp2p20o ()
Conway notationdA10
Elements
Faces20 kites
Edges20+20
Vertices2+20
Vertex figure2 decagons, 20 triangles
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left({\frac {2-3{\sqrt {5}}-2{\sqrt {125+38{\sqrt {5}}}}}{41}}\right)\approx 145.25344^{\circ }}$
Central density1
Number of external pieces20
Level of complexity4
Related polytopes
ArmyDat
RegimentDat
DualDecagonal antiprism
ConjugateDecagrammic antitegum
Abstract & topological properties
Flag count160
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(I2(20)×A1)/2, order 40
ConvexYes
NatureTame

The decagonal antitegum, also known as the decagonal trapezohedron, is an antitegum based on the decagon, constructed as the dual of a decagonal antiprism. It has 20 kites as faces, with 2 order–10 and 20 order–3 vertices. .

Each face of this polyhedron is a kite with its longer edges ${\displaystyle 3+{\sqrt {5}}+{\sqrt {\frac {25+11{\sqrt {5}}}{2}}}\approx 10.21586}$ times the length of its shorter edges.