Square pyramid

Infobox Polyhedron with net

---

Polyhedron_Type=Johnson
J₉₂ - J₁ - J₂
Face_List=4 triangles
1 square
Edge_Count=8
Vertex_Count=5
Symmetry_Group="C"_4v
Vertex_List=4(3².4)
(3⁴)
Dual=self
Property_List=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 (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::$A=(1+sqrt\{3\})a^2$:

Other square pyramids

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: :$V=\{1over3\}l^2h.$

Related polyhedra

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

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* [http://polyhedra.org/poly/show/45/square_pyramid Square Pyramid] -- Interactive Polyhedron Model
* [http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] www.georgehart.com: The Encyclopedia of Polyhedra (VRML [http://www.georgehart.com/virtual-polyhedra/vrml/square_pyramid_(J1).wrl model] )