J92 – J1 – J2
|Symmetry group||C4v, , (*44)|
|Rotation group||C4, +, (44)|
Johnson solid (J1)
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.
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:
|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)