Square pyramid

The square pyramid, or squippy, is a pyramid with a square base and 4 triangles as sides. The version with equilateral triangles as sides is the first of the 92 Johnson solids (J1). In what follows, this is usually what is meant by a "square pyramid", even though other variants with isosceles triangles as sides exist.

Two square pyramids can be joined together at their square base to form a regular octahedron. As such it can also be thought of as a diminished octahedron.

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


 * (±$\sqrt{2}$/2, 0, 0),
 * (0, ±$\sqrt{2}$/2, 0),
 * (0, 0, $\sqrt{2}$/2).

Related polyhedra
A cube can be attached to the base of a square pyramid to form the elongated square pyramid. If a square antiprism is attached instead, the result is the gyroelongated square pyramid.