# Enneagonal tegum

Enneagonal tegum
Rank3
TypeUniform dual
Notation
Bowers style acronymEt
Coxeter diagramm2m9o ()
Elements
Faces18 isosceles triangles
Edges9+18
Vertices2+9
Vertex figure2 enneagons, 9 squares
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left({\frac {\sin ^{2}{\frac {\pi }{9}}-1}{\sin ^{2}{\frac {\pi }{9}}+1}}\right)\approx 142.23656^{\circ }}$
Central density1
Number of external pieces18
Level of complexity3
Related polytopes
ArmyEt
RegimentEt
DualEnneagonal prism
ConjugatesEnneagrammic tegum, Great enneagrammic tegum
Abstract & topological properties
Flag count108
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryI2(9)×A1, order 36
ConvexYes
NatureTame

The enneagonal tegum, also called an enneagonal bipyramid, is a tegum with an enneagon as the midsection, constructed as the dual of an enneagonal prism. It has 18 isosceles triangles as faces, with 2 order–9 and 9 order–4 vertices. .

In the variant obtained as the dual of a uniform enneagonal prism, the side edges are ${\displaystyle {\frac {1}{2\sin ^{2}{\frac {\pi }{9}}}}\approx 4.27432}$ times the length of the edges of the base enneagon. Each face has apex angle ${\displaystyle \arccos \left(1-2\sin ^{4}{\frac {\pi }{9}}\right)\approx 13.43543^{\circ }}$ and base angles ${\displaystyle \arccos \left(\sin ^{2}{\frac {\pi }{9}}\right)\approx 83.28229^{\circ }}$. If the base enneagon has edge length 1, its height is ${\displaystyle {\frac {\cos {\frac {\pi }{9}}}{\sin ^{2}{\frac {\pi }{9}}}}\approx 8.03309}$.