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Square pyramid |
| Square pyramid | |
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| Type | Johnson J92 - J1 - J2 |
| Faces | 4 triangles 1 square |
| Edges | 8 |
| Vertices | 5 |
| Vertex configuration | 4(32.4) (34) |
| Symmetry group | C4v |
| Dual polyhedron | self |
| Properties | convex |
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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.
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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.
The Johnson square pyramid can be characterized by a single edge-length parameter a. The area A (including all five faces) and the volume V of such a pyramid are:
Other square pyramids, such as the have isosceles triangle sides. For example the Great Pyramid of Giza, has isosceles triangles of base 756 feet and slant height 719 feet. That pyramid has the interesting property that the slant height (along the bisector of a face) is very nearly equal to the golden ratio times the height, in which case the area of each triangular face is equal to the square of the pyramid's height.
For square pyramids in general, with base length l and height h, the volume is:
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| 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. |
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 W5.
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