Enneagonal tegum

The enneagonal tegum or et, 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 $$\frac{1}{2\sin^2\frac\pi9} ≈ 4.27432$$ times the length of the edges of the base enneagon. Each face has apex angle $$\arccos\left(1-2\sin^4\frac\pi9\right) \approx 13.43543°$$ and base angles $$\arccos\left(\sin^2\frac\pi9\right) \approx 83.28229°$$. If the base enneagon has edge length 1, its height is $$\frac{\cos\frac\pi9}{\sin^2\frac\pi9} ≈ 8.03309$$.