Pentagrammic pyramid

The pentagrammic pyramid, or stappy, is a pyramid with a pentagrammic base and 5 triangles as sides.

It is the vertex-first cap of the great icosahedron. A regular great icosahedron can be constructed by attaching two pentagrammic pyramids to the bases of a pentagrammic retroprism.

Vertex coordinates
A pentagrammic pyramid of edge length 1 has the following vertices:


 * (±1/2, -$\sqrt{5}$, 0),
 * (±($\sqrt{(5-2√5)/20}$-1)/4, $\sqrt{5}$, 0),
 * (0, $\sqrt{(5-√5)/40}$, 0),
 * (0, 0, $\sqrt{(5-√5)/10}$).

Related polyhedra
Two pentagonal pyramids can be attached at their bases to form a pentagrammic bipyramid.