View source for Augmented triangular prism

{{Short description|49th Johnson solid}}
{{Infobox polyhedron
|image=augmented triangular prism.png
|type=[[Johnson solid|Johnson]]<br>{{math|[[Gyroelongated pentagonal birotunda|''J''{{sub|48}}]] – '''''J''{{sub|49}}''' – [[Biaugmented triangular prism|''J''{{sub|50}}]]}}
|faces=3x2 [[Triangle|triangle]]s<br>2 squares
|edges=13
|vertices=7
|symmetry={{math|''C''{{sub|2v}}}}
|vertex_config={{math|2(3.4{{sup|2}})<br>1(3{{sup|4}})<br>4(3{{sup|3}}.4)}}
|dual=monolaterotruncated triangular bipyramid
|properties=[[Convex polytope|convex]]
|net=Johnson solid 49 net.png
}}

In [[Geometry|geometry]], the '''augmented triangular prism''' is one of the [[Johnson solid]]s ({{math|''J''{{sub|49}}}}). As the name suggests, it can be constructed by augmenting a triangular [[Prism (geometry)|prism]] by attaching a [[Square pyramid|square pyramid]] ({{math|''J''{{sub|1}}}}) to one of its equatorial faces. The resulting solid bears a superficial resemblance to the [[Gyrobifastigium|gyrobifastigium]] ({{math|''J''{{sub|26}}}}), 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 {{math|2-''p''}} [[Duoprism#Duoantiprism|duoantiprism]] (if {{math|''p'' ≥ 2}}). Despite the fact that {{math|1=''p'' = 3}} would yield a geometrically identical equivalent to the Johnson solid, it lacks a [[Circumscribed sphere|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}}

==External links==
* {{MathWorld | urlname=JohnsonSolid | title=Johnson Solid}}
** {{MathWorld | urlname=AugmentedTriangularPrism | title=Augmented triangular prism }}

{{Johnson solids navigator}}

[[Category:Johnson solids]]



{{Sourceattribution|Augmented triangular prism}}