Elongated triangular pyramid: Difference between revisions

Revision as of 16:12, 16 October 2021

Revision as of 12:52, 9 June 2022

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{{Short description|7th Johnson solid (7 faces)}}

{{Infobox polyhedron

| image = elongated_triangular_pyramid.png

| type = [[Johnson solid|Johnson]]<br>{{math|[[pentagonal rotunda|''J<''{{sub>|6</sub>}}]] -– ''''' J<''{{sub>|7</sub>}}''' -– [[elongated square pyramid|''J<''{{sub>|8</sub>}}]]}}

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

| edges = 12

| vertices = 7

| symmetry = ''{{math|C''<{{sub>|3v</sub>}}, [3], (*33)}}

| rotation_group = ''{{math|C''<{{sub>|3</sub>}}, [3]<{{sup>|+</sup>}}, (33)}}

| vertex_config = {{math|1(3<{{sup>|3</sup>}})<br>3(3.4<{{sup>|2</sup>}})<br>3(3<{{sup>|2</sup>}}.4<{{sup>|2</sup>}})}}

| dual = self

| properties = [[convex set|convex]]

| net = Elongated Triangular Pyramid Net.svg

}}

[[File:Tetraedro elongado 3D.stl|thumb|Johnson solid {{math|''J<''{{sub>|7</sub>}}}}.]]

In [[geometry]], the '''elongated triangular pyramid''' is one of the [[Johnson solid]]s ({{math|''J''<{{sub>|7</sub>}}}}). 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]].

{{Johnson solid}}