Decagonal tegum

The decagonal tegum or det, also called a decagonal dipyramid, is a tegum with a decagon as the midsection, constructed as the dual of a decagonal prism. It has 20 isosceles triangles as faces, with 2 order–10 and 10 order–4 vertices.

In the variant obtained as the dual of a uniform decagonal prism, the side edges are $$3+\sqrt5 ≈ 5.23607$$ times the length of the edges of the base decagon. Each face has apex angle $$\arccos\left(3\frac{3+\sqrt5}{16}\right) ≈ 10.95922°$$ and base angles $$\arccos\left(\frac{3-\sqrt5}{8}\right) \approx 84.52039°$$. If the base decagon has edge length 1, its height is $$\sqrt{50+22\sqrt5} ≈ 9.95959$$.