Hexagonal duotegmatic alterprism

The hexagonal duotegmatic alterprism is a convex isogonal polyteron that consists of 2 hexagonal duotegums and 72 isosceles triangular-triangular duotegums. 1 hexagonal duotegum and 18 isosceles triangular-triangular duotegums join at each vertex. It can be formed as an alterprism of a hexagonal duotegum, or as the hull of two opposite hexagonal disphenoids.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{1+\sqrt3}$$ ≈ 1:1.65289.