Augmented triangular prism: Difference between revisions

Revision as of 07:51, 22 June 2022

Revision as of 13:32, 13 March 2024

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In [[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]] ({{math|''J''{{sub|1}}}}) to one of its equatorial faces. The resulting solid bears a superficial resemblance to the [[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]] 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}}