# Square pyramid

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Square pyramid | |
---|---|

Type |
Johnson J _{92} - J - J_{1}_{2} |

Faces |
4 triangles 1 square |

Edges | 8 |

Vertices | 5 |

Vertex configuration |
4(3^{2}.4)(3 ^{4}) |

Symmetry group |
C_{4v} |

Dual polyhedron | self |

Properties | convex |

Net | |

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 *C*_{4v} symmetry.

## Johnson solid (J1)

If the sides are all equilateral triangles, the pyramid is one of the Johnson solids (J_{1}). The 92 Johnson solids were named and described by Norman Johnson 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

A regular octahedron can be considered a square bipyramid, with two Johnson square pyramids connected base-to-base. | The tetrakis hexahedron can be considered a cube with short square pyramids added to each face. |

## Topology

Like all pyramids, the square pyramid is self-dual, containing the same number of vertices and faces.

A square pyramid can be represented by the Wheel graph W_{5}.

## See also

- Bipyramid - A bipyramid is two pyramids connected base to base.

## External links

- Template:Mathworld2
- Weisstein, Eric W., "Square pyramid" from MathWorld.
- Square Pyramid -- Interactive Polyhedron Model
- Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra (VRML model)

This polyhedron-related article is a stub. You can help Math Wiki by expanding it. |

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