Triangular triswirlprism

The triangular triswirlprism is a convex isogonal polychoron that consists of 18 triangular antiprisms and 54 phyllic disphenoids. It is the simplest nontrivial member of the duoprismatic swirlprisms.

Vertex coordinates
The vertices of a triangular triswirlprism, constructed as the convex hull of three 3-3 duoprisms of edge length 1, centered at the origin, are given by:


 * (0, $\sqrt{3}$/3, 0, $\sqrt{3}$/3),
 * (0, $\sqrt{3}$/3, ±1/2, –$\sqrt{3}$/6),
 * (±1/2, –$\sqrt{3}$/6, 0, $\sqrt{3}$/3),
 * (±1/2, –$\sqrt{3}$/6, ±1/2, –$\sqrt{3}$/6),
 * ($\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, $\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3),
 * ($\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, $\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * ($\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, –$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3)
 * ($\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, $\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3),
 * ($\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, $\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * ($\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, –$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3),
 * (–$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, $\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3),
 * (–$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, $\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * (–$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, –$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3),
 * ($\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, $\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3),
 * ($\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, –$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * ($\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, –$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3),
 * (–$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, $\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3),
 * (–$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, –$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * (–$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, –$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3),
 * (–$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, $\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3),
 * (–$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, –$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * (–$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, –$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3).