Great enneagrammic duoprism

The great enneagrammic duoprism or gastedip, also known as the great enneagrammic-great enneagrammic duoprism, the 9/4 duoprism or the 9/4-9/4 duoprism, is a noble uniform duoprism that consists of 18 great enneagrammic prisms and 81 vertices.

Vertex coordinates
The vertex coordinates of a great enneagrammic duoprism, centered at the origin and with edge length 2sin(4π/9), are given by:
 * (1, 0, 1, 0),
 * (1, 0, cos(2π/9), ±sin(2π/9)),
 * (1, 0, cos(4π/9), ±sin(4π/9)),
 * (1, 0, cos(6π/9), ±sin(6π/9)),
 * (1, 0, cos(8π/9), ±sin(8π/9)),
 * (cos(2π/9), ±sin(2π/9), 1, 0),
 * (cos(2π/9), ±sin(2π/9), cos(2π/9), ±sin(2π/9)),
 * (cos(2π/9), ±sin(2π/9), cos(4π/9), ±sin(4π/9)),
 * (cos(2π/9), ±sin(2π/9), cos(6π/9), ±sin(6π/9)),
 * (cos(2π/9), ±sin(2π/9), cos(8π/9), ±sin(8π/9)),
 * (cos(4π/9), ±sin(4π/9), 1, 0),
 * (cos(4π/9), ±sin(4π/9), cos(2π/9), ±sin(2π/9)),
 * (cos(4π/9), ±sin(4π/9), cos(4π/9), ±sin(4π/9)),
 * (cos(4π/9), ±sin(4π/9), cos(6π/9), ±sin(6π/9)),
 * (cos(4π/9), ±sin(4π/9), cos(8π/9), ±sin(8π/9)),
 * (cos(6π/9), ±sin(6π/9), 1, 0),
 * (cos(6π/9), ±sin(6π/9), cos(2π/9), ±sin(2π/9)),
 * (cos(6π/9), ±sin(6π/9), cos(4π/9), ±sin(4π/9)),
 * (cos(6π/9), ±sin(6π/9), cos(6π/9), ±sin(6π/9)),
 * (cos(6π/9), ±sin(6π/9), cos(8π/9), ±sin(8π/9)),
 * (cos(8π/9), ±sin(8π/9), 1, 0),
 * (cos(8π/9), ±sin(8π/9), cos(2π/9), ±sin(2π/9)),
 * (cos(8π/9), ±sin(8π/9), cos(4π/9), ±sin(4π/9)),
 * (cos(8π/9), ±sin(8π/9), cos(6π/9), ±sin(6π/9)),
 * (cos(8π/9), ±sin(8π/9), cos(8π/9), ±sin(8π/9)).