J92 – J1 – J2
|Symmetry group||C4v, , (*44)|
|Rotation group||C4, +, (44)|
A Johnson solid is one of 92 strictly convex regular-faced polyhedra, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. They are named by Norman Johnson who first enumerated the set in 1966.
Johnson solid (J1)
The Johnson square pyramid can be characterized by a single edge-length parameter a. 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:
Other square pyramids
Other square pyramids have isosceles triangle sides.
For square pyramids in general, with base length l and height h, the surface area and volume are:
|Tetrahedron||Square pyramid||Pentagonal pyramid||Hexagonal pyramid|
|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|
Like all pyramids, the square pyramid is self-dual, having the same number of vertices as faces.
A square pyramid can be represented by the Wheel graph W5.
- Eric W. Weisstein, Square pyramid (Johnson solid) at MathWorld
- Weisstein, Eric W., "Wheel graph", MathWorld.
- Square Pyramid -- Interactive Polyhedron Model
- Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra (VRML model)