Elongated triangular pyramid: Difference between revisions

Revision as of 08:18, 23 March 2013

Revision as of 04:41, 30 March 2013

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{{Infobox Polyhedron with net|

|Image_File Image_File= elongated_triangular_pyramid.png|

|Polyhedron_Type Polyhedron_Type= [[Johnson solid|Johnson]]<br>[[pentagonal rotunda|J₆]] -''' J₇''' - [[elongated square pyramid|J₈]]|

|Face_List Face_List= 1+3 [[triangle]]s<br>3 [[Square (geometry)|square]]s|

|Edge_Count = 12

Edge_Count=12|

|Vertex_Count = 7

Vertex_Count=7|

|Symmetry_Group Symmetry_Group= ''C''_3v, [3], (*33)|

|Rotation_Group Rotation_Group= ''C''₃, [3]⁺, (33)|

|Vertex_List Vertex_List= 1(3³)<br>3(3.4²)<br>3(3².4²)|

|Dual Dual= self|

|Property_List Property_List= [[convex set|convex]]|

|Net_Image_File Net_Image_File= Elongated Triangular Pyramid Net.svg

}}

In [[geometry]], the '''elongated triangular pyramid''' is one of the [[Johnson solid]]s (''J''₇). [[Norman Johnson (mathematician)|Norman Johnson]] discovered elongated triangular pyramids.{{Citation needed|seems a silly claim|date=November 2010}} As the name suggests, it can be constructed by elongating a [[tetrahedron]] by attaching a [[triangular prism]] to its base. Like any elongated [[pyramid]], the resulting solid is topologically (but not geometrically) self-[[dual polyhedron|dual]].

The 92 Johnson solids were named and described by Norman Johnson in 1966.

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If the edges are not the same length, use the individual formulae for the tetrahedron and triangular prism separately, and add the results together.

=== Dual polyhedron ===

=== Dual polyhedron ===

The dual of the elongated triangular pyramid has 7 faces: 4 triangular, and 3 trapezoidal.

{| class=wikitable width=320

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==External links==

* {{mathworld | urlname = ElongatedTriangularPyramid | title = Elongated triangular pyramid }}

* {{mathworld | urlname = JohnsonSolid | title = Johnson solid}}

{{DEFAULTSORT:Elongated Triangular Pyramid}}

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[[Category:Self-dual polyhedra]]

[[Category:Pyramids and bipyramids]]

{{Polyhedron-stub}}