Elongated triangular cupola

The elongated triangular cupola is one of the 92 Johnson solids (J18). It consists of 1+3 triangles, 3+3+3 squares, and 1 hexagon. It can be constructed by attaching a hexagonal prism to the hexagonal base of the triangular cupola.

If a second cupola is attached to the other hexagonal base of the prism in the same orientation, the result is the elongated triangular orthobicupola. If the second cupola is rotated 60º instead, rhe result is the elongated triangular gyrobicupola.

Vertex coordinates
An elongated triangular cupola of edge length 1 has the following vertices:
 * $$\left(\pm\frac12,\,\pm\frac{\sqrt3}{2},\,\pm\frac12\right),$$
 * $$\left(\pm1,\,0,\,\pm\frac12\right),$$
 * $$\left(\pm\frac12,\,-\frac{\sqrt3}{6},\,\frac{3+2\sqrt6}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,\frac{3+2\sqrt6}{6}\right).$$

Related polytopes
The elongated triangular cupola can be tunnelled with a triangular cupola and a triangular prism to form a quasi-convex Stewart toroid, the tunnelled elongated triangular cupola. This is the only quasi-convex Stewart toroid with the elongated triangular cupola as its convex hull.