Dodecagonal tegum

The dodecagonal tegum or twit, also called a dodecagonal dipyramib, is a tegum with a dodecagon as the midsection, constructed as the dual of a dodecagonal prism. It has 24 isosceles triangles as faces, with 2 order–12 and 12 order–4 vertices.

In the variant obtained as the dual of a uniform dodecagonal prism, the side edges are $$4+2\sqrt3 \approx 7.46410$$ times the length of the edges of the base dodecagon. Each face has apex angle $$\arccos\left(\frac{1+4\sqrt3}{8}\right) \approx 7.68193^\circ$$ and base angles $$\arccos\left(\frac{2-\sqrt3}{4}\right) \approx 86.15903^\circ$$. If the base dodecagon has edge length 1, its height is $$2\sqrt{26+15\sqrt3} \approx 14.41954$$.