Hexagonal tegum

The hexagonal tegum or hat, also called a hexagonal bipyramid, is a tegum with a hexagon as the midsection, constructed as the dual of a hexagonal prism. It has 12 isosceles triangles as faces, with 2 order–6 and 6 order–4 vertices. .

In the variant obtained as the dual of a uniform hexagonal prism, the side edges are exactly 2 times the length of the edges of the base hexagon. Each face has apex angle $$\arccos\left(\frac78\right) \approx 28.95502°$$ and base angles $$\arccos\left(\frac14\right) \approx 75.52249°$$. If the base hexagon has edge length 1, its height is $$2\sqrt3 ≈ 3.46410$$.