Octagonal tegum

The octagonal bipyramid or odpy, also called an octagonal dipyramid, is a bipyramid with an octagon as the midsection, constructed as the dual of an octagonal prism. It has 16 isosceles triangles as faces, with 2 order–8 and 8 order–4 vertices. .

In the variant obtained as the dual of a uniform octagonal prism, the side edges are $$2+\sqrt2 ≈ 3.41421$$ times the length of the edges of the base octagon. Each face has apex angle $$\arccos\left(\frac{1+2\sqrt2}{4}\right) \approx 16.84212°$$ and base angles $$\arccos\left(\frac{2-\sqrt2}{4}\right) \approx 81.57894°$$. If the base octagon has edge length 1, its height is $$\sqrt{20+14\sqrt2} ≈ 6.30864$$.