Hexagonal triotegum

The hexagonal triotegum or hittit is a noble triotegum that consists of 216 digonal trisphenoids and 18 vertices. 72 facets join at each vertex. It is also the 18-5-7 step prism.

The ratio between the longest and shortest edges is 1:$$\sqrt2$$ ≈ 1:1.41421.