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| {{Infobox polyhedron
| | Her title is Felicidad Ahmad. The thing she adores most is flower arranging and she is attempting to make it a profession. My occupation is a messenger. Delaware is the only place I've been residing in.<br><br>My website :: extended auto warranty, [http://Games.Any.ge/profile/sin08 made a post], |
| |image=Square pyramid.png
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| |type=[[Johnson solid|Johnson]]<br>[[triangular hebesphenorotunda|J<sub>92</sub>]] – '''J<sub>1</sub>''' – [[pentagonal pyramid|J<sub>2</sub>]]
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| |faces=4 [[triangle]]s<br>1 [[Square (geometry)|square]]
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| |edges=8
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| |vertices=5
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| |symmetry=''C''<sub>4v</sub>, [4], (*44)
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| |rotation_group=''C''<sub>4</sub>, [4]<sup>+</sup>, (44)
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| |vertex_config=4(3<sup>2</sup>.4)<br>(3<sup>4</sup>)
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| |dual=self
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| |properties=[[convex set|convex]]
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| |net=Square pyramid net.svg
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| }}
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| In [[geometry]], a '''square pyramid''' is a [[Pyramid (geometry)|pyramid]] having a [[square (geometry)|square]] base. If the [[Apex (geometry)|apex]] is perpendicularly above the center of the square, it will have ''C''<sub>4v</sub> symmetry.
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| {{Johnson_solid}}
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| == Johnson solid (J1) ==
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| If the sides are all [[equilateral triangle]]s, the pyramid is one of the [[Johnson solid]]s (J<sub>1</sub>). The 92 Johnson solids were named and described by [[Norman Johnson (mathematician)|Norman Johnson]] in 1966. galen verg...
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| 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:
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| :<math>H=\frac{1}{\sqrt{2}}a</math>
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| :<math>A=(1+\sqrt{3})a^2</math>
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| :<math>V=\frac{\sqrt{2}}{6}a^3.</math>
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| == Other square pyramids ==
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| Other square pyramids have [[isosceles]] triangle sides.
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| For square pyramids in general, with base length ''l'' and height ''h'', the surface area and volume are:
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| :<math>A=l^2+l\sqrt{l^2+(2h)^2}</math>
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| :<math>V=\frac{1}{3}l^2h.</math>
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| == Related polyhedra ==
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| {{Pyramids}}
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| {| class=wikitable width=480
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| ![[File:Square bipyramid.png|160px]]
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| ![[File:Tetrakishexahedron.jpg|160px]]
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| ![[File:Usech kvadrat piramid.png|160px]]
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| |-
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| |align=center|A regular [[octahedron]] can be considered a square [[bipyramid]], i.e. two Johnson square pyramids connected base-to-base.
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| |The [[tetrakis hexahedron]] can be constructed from a [[cube]] with short square pyramids added to each face.
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| |Square [[frustum]] is a square pyramid with the apex truncated.
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| |}
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| === Dual polyhedron ===
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| The square pyramid is topologically a [[self-dual polyhedron]]. The dual edge lengths are different due to the [[polar reciprocation]].
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| {| class=wikitable width=320
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| |- valign=top
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| !Dual Square pyramid
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| !Net of dual
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| |- valign=top
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| |[[File:Dual square pyramid.png|160px]]
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| |[[File:Dual square pyramid net.png|160px]]
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| |}
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| == Topology ==
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| Like all pyramids, the square pyramid is [[Self-dual polyhedron|self-dual]], having the same number of vertices as faces.
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| A square pyramid can be represented by the [[Wheel graph]] W<sub>5</sub>.
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| ==External links==
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| * {{Mathworld2 | urlname = SquarePyramid | title = Square pyramid | urlname2 = JohnsonSolid | title2 = Johnson solid }}
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| * {{Mathworld | urlname = WheelGraph | title = Wheel graph}}
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| * [http://polyhedra.org/poly/show/45/square_pyramid Square Pyramid] -- Interactive Polyhedron Model
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| *[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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| {{Polyhedron navigator}}
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| [[Category:Self-dual polyhedra]]
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| [[Category:Prismatoid polyhedra]]
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| [[Category:Johnson solids]]
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| [[Category:Pyramids and bipyramids]]
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Her title is Felicidad Ahmad. The thing she adores most is flower arranging and she is attempting to make it a profession. My occupation is a messenger. Delaware is the only place I've been residing in.
My website :: extended auto warranty, made a post,