Augmented triangular prism: Difference between revisions

Revision as of 14:27, 25 August 2021

Revision as of 22:31, 13 June 2022

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{{Short description|49th Johnson solid}}

{{Infobox polyhedron

|image=augmented triangular prism.png

|type=[[Johnson solid|Johnson]]<br>{{math|[[gyroelongated pentagonal birotunda|''J<''{{sub>|48</sub>}}]] -– '''''J<''{{sub>|49</sub>}}''' -– [[biaugmented triangular prism|''J<''{{sub>|50</sub>}}]]}}

|faces=3x2 [[triangle]]s<br>2 [[Square (geometry)|square]]s

|edges=13

|vertices=7

|symmetry={{math|''C''<{{sub>|2v</sub>}}}}

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

|dual=monolaterotruncated triangular bipyramid

|properties=[[Convex setpolytope|convex]]

|net=Johnson solid 49 net.png

}}

In [[geometry]], the '''augmented triangular prism''' is one of the [[Johnson solid]]s ({{math|''J''<{{sub>|49</sub>}}}}). As the name suggests, it can be constructed by augmenting a triangular [[prism (geometry)|prism]] by attaching a [[square pyramid]] ({{math|''J''<{{sub>|1</sub>}}}}) to one of its equatorial faces. The resulting solid bears a superficial resemblance to the [[gyrobifastigium]] ({{math|''J''<{{sub>|26</sub>}}}}), the difference being that the latter is constructed by attaching a second triangular prism, rather than a square pyramid.

It is also the vertex figure of the nonuniform [[Duoprism#Duoantiprism{{math|2-''p''}} [[Duoprism#Duoantiprism|duoantiprism]] (if {{math|''p'' is greater than&ge; 2}}). Despite the fact that {{math|1=''p'' = 3}} would yield a geometrically identical equivalent to the Johnson solid, it lacks a [[circumscribed sphere]] that touches all vertices.

Its dual, a triangular bipyramid with one of its 4-valence vertices truncated, can be found as cells of the {{math|2-''p''}} duoantitegums (duals of the {{math|2-''p''}} duoantiprisms).

{{Johnson solid}}