# Enneagonal antitegum

The enneagonal antitegum, also known as the enneagonal trapezohedron, is an antitegum based on the enneagon, constructed as the dual of an enneagonal antiprism. It has 18 kites as faces, with 2 order–9 and 18 order–3 vertices.

Enneagonal antitegum
Rank3
TypeUniform dual
Notation
Bowers style acronymEat
Coxeter diagramp2p18o ()
Conway notationdA9
Elements
Faces18 kites
Edges18+18
Vertices2+18
Vertex figure2 enneagons, 14 triangles
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left(1+{\frac {2}{2\cos {\frac {\pi }{9}}-3}}\right)\approx 141.69614^{\circ }}$
Central density1
Number of external pieces18
Level of complexity4
Related polytopes
ArmyEat
RegimentEat
DualEnneagonal antiprism
ConjugateGreat enneagrammic concave antitegum
Abstract & topological properties
Flag count144
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(I2(18)×A1)/2, order 36
ConvexYes
NatureTame

Each face of this polyhedron is a kite with its longer edges ${\displaystyle {\frac {2+4\cos {\frac {\pi }{9}}+\csc {\frac {\pi }{18}}+{\sqrt {3}}\csc {\frac {\pi }{9}}}{2}}\approx 8.29086}$ times the length of its shorter edges.