J92 – J1 – J2
|Vertices||Trryru Ru], (*44)|
|Rotation group||C4, +, (44)|
In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid, and has C4v symmetry. If all edges are equal, it is an equilateral square pyramid, the Johnson solid J1.
General square pyramid
A possibly oblique square pyramid with base length l and perpendicular height h has volume:
Right square pyramid
In a right square pyramid, all the lateral edges have the same length, and the sides other than the base are congruent isosceles triangles.
A right square pyramid with base length l and height h has surface area and volume:
The lateral edge length is:
and the slant height is:
The dihedral angles are:
- between the base and a side: ;
- between two sides: .
Equilateral square pyramid, Johnson solid J1 
The Johnson square pyramid can be characterized by a single edge-length parameter l. The height h (from the midpoint of the square to the apex), the surface area A (including all five faces), and the volume V of such a pyramid are:
A square pyramid can be represented by the Wheel graph W5.
Related polyhedra and honeycombs
|A regular octahedron can be considered a square bipyramid, i.e. two Johnson square pyramids connected base-to-base.||The tetrakis hexahedron can be constructed from a cube with short square pyramids added to each face.||Square frustum is a square pyramid with the apex truncated.|
|Dual Square pyramid||Net of dual|
- Franz Hocevar, Solid Geometry, 1903, p. 44