Type JohnsonJ92 – J1 – J2 Schläfli symbol ( ) ∨ {4} Rotation group C4, [4], (44) Volume 1/3 × l² × h Number of faces 5 Base shape Square | Vertex configuration 4(3.4)(3) Symmetry group C4v, [4], (*44) Dual polyhedron self Number of edges 8 Number of vertices 5 | |
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Surface area a × (1 + 2 ×√((a/2)² + h²) Shapes with similar faces Cube, Cuboid, Triangular prism | ||
Pyramid how to draw a square pyramid
In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry.
Contents
- Pyramid how to draw a square pyramid
- Square pyramid part 1
- Johnson solid J1
- Other square pyramids
- Related polyhedra and honeycombs
- Dual polyhedron
- Topology
- References
Square pyramid part 1
Johnson solid (J1)
If the sides are all equilateral triangles, the pyramid is one of the Johnson solids (J1). The 92 Johnson solids were named and described by Norman Johnson in 1966.
A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra 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:
Related polyhedra and honeycombs
Square pyramids fill space with tetrahedra, truncated cubes or cuboctahedra.
Dual polyhedron
The square pyramid is topologically a self-dual polyhedron. The dual edge lengths are different due to the polar reciprocation.
Topology
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.