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, unless otherwise specified, this is what will be 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.

In addition to being a point atop a square, the square pyramid has a second representation as a segmentohedron, as a dyad atop a triangle, obtained from removing a vertex from the octahedron.

Abstractly, the square pyramid is the simplest non-regular polytope overall.

Vertex coordinates
Coordinates for a square pyramid of edge length 1 are given by:


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

Representations
A square pyramid has the following Coxeter diagrams:


 * ox4oo&#x (full symmetry)
 * ox ox&#x (rectangle pyramid)
 * oxx&#x (isosceles trapezoid pyramid)

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.