Triaugmented triangular prism: Difference between revisions

Revision as of 20:51, 27 November 2022

Revision as of 07:46, 28 November 2022

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==Construction==

[[File:J51 triaugmented triangular prism.stl|thumb|3D model of the triaugmented triangular prism]]

The triaugmented triangular prism can be constructed by attaching [[equilateral square pyramid]]s to each of the three square faces of a [[triangular prism]].{{r|pugh}} These pyramids cover each square, replacing it with four [[equilateral triangle]]s, so that the resulting polyhedron compriseshas 14 equilateral triangles as its faces. A polyhedron with only equilateral triangles as faces, like this one, is called a [[deltahedron]]. There are only eight different [[Convex set|convex]] deltahedra, one of which is the triaugmented triangular prism.{{r|fw47|cundy}} More generally, the convex polyhedra in which all faces are [[regular polygon]]s are called the [[Johnson solid]]s, and every convex deltahedron is a Johnson solid. The triaugmented triangular prism is numbered among the Johnson solids {{nowrap|as <math>J_{51}</math>.{{r|francis}}}}

One possible system of [[Cartesian coordinates]] for the vertices of a triaugmented triangular prism, giving it edge length 2, is:{{r|shdc}}