Heptagonal tegum

The heptagonal tegum or het, also called a heptagonal bipyramid, is a tegum with a heptagon as the midsection, constructed as the dual of a heptagonal prism. It has 14 isosceles triangles as faces, with 2 order–7 and 7 order–4 vertices.

In the variant obtained as the dual of a uniform heptagonal prism, the side edges are $$\frac{1}{2\sin^2\frac\pi7} \approx 2.65597$$ times the length of the edges of the base heptagon. Each face has apex angle $$\arccos\left(1-2\sin^4\frac\pi7\right) \approx 21.70194^\circ$$ and base angles $$\arccos\left(\sin^2\frac\pi7\right) \approx 79.14903^\circ$$. If the base heptagon has edge length 1, its height is $$\frac{\cos\frac\pi7}{\sin^2\frac\pi7} \approx 4.78589$$.