Augmented triangular prism: Difference between revisions

Revision as of 14:06, 13 March 2024

Revision as of 14:11, 13 March 2024

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{{Short description|49th Johnson solid}}

{{Infobox polyhedron

| image =augmented 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 6 [[triangle]]s<br>2 [[Square (geometry)|square]]s

| edges = 13

| vertices = 7

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

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

&2 \times (3 \times 4^2) \, + \\

|dual=monolaterotruncated triangular bipyramid

&1 \times (3^4) \, + \\

|properties=[[Convex polytope|convex]]

&4 \times (3^3 \times 4) \end{align} </math>

|net=Johnson solid 49 net.png

| properties = [[Convex polytope|convex]]

| net = Johnson solid 49 net.png

}}

In [[geometry]], the '''augmented triangular prism''' is onea of the [[Johnson solid]]s ({{math|''J''{{sub|49}}}}). As the name suggests, it can bepolyhedron constructed by augmentingattaching a triangularan [[prismequilateral (geometry)|prism]] by attaching a [[square pyramid]] ({{math|''J''{{sub|1}}}})onto tothe onesquare face of itsa equatorial[[triangular facesprism]. TheAs resultinga solidresult, bearsit ais superficialan resemblanceexample to theof [[gyrobifastigiumJohnson solid]] ({{math|''J''{{sub|26}}}}), the difference being that the latter is constructed by attaching a second triangular prism, rather than a square pyramid.

== Construction ==

The augmented triangular prism can be constructed from a [[triangular prism]] by attaching an [[equilateral square pyramid]] to one of its square faces, a process known as [[Augmentation (geometry)|augmentation]].{{r|rajwade}} This square pyramid covers the square face of the prism, so the resulting polyhedron has 6 [[equilateral triangle]]s and 2 [[Square (geometry)|square]]s as its faces.{{r|berman}} A [[Convex set|convex]] polyhedron in which all faces are [[Regular polygon|regular]] is [[Johnson solid]], and the augmented triangular prism is among them, enumerated as 49th Johnson solid <math> J_{49} </math>.{{r|francis}}

== Properties ==