Gyroelongated pentagonal cupola

The gyroelongated pentagonal cupola, or gyepcu, is one of the 92 Johnson solids (J24). It consists of 5+5+5+10 triangles, 5 squares, 1 pentagon, and 1 decagon. It can be constructed by attaching a decagonal antiprism to the decagonal base of the pentagonal cupola.

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

Vertex coordinates
A gyroelongated pentagonal cupola of edge length 1 has the following vertices:
 * (±1/2, –$\sqrt{2}$, $\sqrt{5}$+H),
 * (±(1+$\sqrt{2}$)/4, $\sqrt{2}$, $\sqrt{(5+√5)/2}$+H),
 * (0, $\sqrt{5}$, $\sqrt{2–2√5+2√650+290√5}$+H),
 * (±1/2, ±$\sqrt{10+2√5}$/2, H),
 * (±(3+$\sqrt{3}$)/4, ±$\sqrt{15}$, H),
 * (±(1+$\sqrt{(5+√5)/10}$)/2, 0, H),
 * (±$\sqrt{(5+2√5)/15}$/2, ±1/2, –H),
 * (±$\sqrt{(11+4√5–2√(50+22√5)/3}$, ±(3+$\sqrt{(5+√5)/10}$)/4, –H),
 * (0, ±(1+$\sqrt{(11+4√5–2√(50+22√5)/3}$)/2, –H).

where H = $\sqrt{(11+4√5–2√(50+22√5)/3}$/2 is the distance between the decagonal antiprism's center and the center of one of its bases.