- Square pyramid

Polyhedron_Type=Johnson

J_{92}-**J**- J_{1}_{2}

Face_List=4triangle s

1 square

Edge_Count=8

Vertex_Count=5

Symmetry_Group="C"_{4v}

Vertex_List=4(3^{2}.4)

(3^{4})

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 triangle s, the pyramid is one of theJohnson solid s (J_{1}). The 92 Johnson solids were named and described byNorman Johnson in1966 .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::$A=(1+sqrt\{3\})a^2$:$V=egin\{matrix\}\{sqrt\{2\}over6\}end\{matrix\}a^3$

**Other square pyramids**Other square pyramids, such as the have

isosceles triangle sides. For example theGreat Pyramid of Giza , has isosceles triangles of base 756 feet andslant height 719 feet. That pyramid has the interesting property that the slant height (along the bisector of a face) is very nearly equal to thegolden 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 W_{5}.**See also***

Bipyramid - A bipyramid is two pyramids connected base to base.**External links***

*

* [*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*] )

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