Enneagonal triotegum

The enneagonal triotegum is a noble triotegum that consists of 729 digonal trisphenoids and 27 vertices. 162 facets join at each vertex. It is also the 27-8-10 step prism.

The ratio between the longest and shortest edges is 1:csc(π/9)/$\sqrt{2}$ ≈ 1:2.06744.