Gyroelongated triangular cupola

The gyroelongated triangular cupola, or gyetcu, is one of the 92 Johnson solids (J22). It consists of 1+3+3+3+6 triangles, 3 squares, and 1 hexagon. It can be constructed by attaching a hexagonal antiprism to the hexagonal base of the triangular cupola.

If a second cupola is attached to the other hexagonal base of the antiprism, the result is the gyroelongated triangular bicupola.

Vertex coordinates
A gyroelongated triangular cupola of edge length 1 has the following vertices:
 * (±1/2, –$\sqrt{2}$/6, (2$\sqrt{2}$+3$\sqrt{3}$)/6)
 * (0, $\sqrt{2}$/3, (2$\sqrt{2+2√3}$+3$\sqrt{3}$)/6)
 * (±1/2, ±$\sqrt{3}$/2, $\sqrt{3}$/2)
 * (±1, 0, $\sqrt{3}$/2)
 * (±$\sqrt{3}$/2, ±1/2, –$\sqrt{3}$/2)
 * (0, ±1, –$\sqrt{3}$/2)