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Square pyramid

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Square pyramid
Square pyramid
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
Net
Square pyramid 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 C4v symmetry.

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.

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:

H=\frac{1}{\sqrt{2}}a
A=(1+\sqrt{3})a^2
V=\frac{1}{3}a^3

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=l^2+l\sqrt{l^2+(2h)^2}
V=\frac{1}{3}l^2h.

Related polyhedra

Square bipyramid Tetrakishexahedron
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 W5.

See also

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

External links

eo:Kvadrata piramidoit:Piramide quadrata

nl:Vierkante piramidept:Pirâmide quadrada th:พีระมิดสี่เหลี่ยมจัตุรัส

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