Triaugmented triangular prism: Difference between revisions

Revision as of 02:26, 9 December 2022

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The '''triaugmented triangular prism''', in geometry, is a [[convex polyhedron]] with 14 [[equilateral triangle]]s as its faces. It can be constructed from a [[triangular prism]] by attaching [[equilateral square pyramid]]s to each of its three square faces. The same shape is also called the '''tetrakis triangular prism''',{{r|triggshdc}} '''tricapped trigonal prism''',{{r|kepert}} '''tetracaidecadeltahedron''',{{r|burgiel|pugh}} or '''tetrakaidecadeltahedron''';{{r|shdc}} these last names mean a polyhedron with 14 triangular faces. It is an example of a [[deltahedron]] and of a [[Johnson solid]].

The same shape is also called the '''tetrakis triangular prism''',{{r|shdc}} '''tricapped trigonal prism''',{{r|kepert}} '''tetracaidecadeltahedron''',{{r|burgiel|pugh}} or '''tetrakaidecadeltahedron''';{{r|shdc}} these last names mean a polyhedron with 14 triangular faces. It is an example of a [[deltahedron]] and of a [[Johnson solid]].

The edges and vertices of the triaugmented triangular prism form a [[maximal planar graph]] with 9 vertices and 21 edges, called the '''Fritsch graph'''. It was used by Rudolf and Gerda Fritsch to show that [[Alfred Kempe]]'s attempted proof of the [[four color theorem]] was incorrect. The Fritsch graph is one of only six graphs in which every [[Neighbourhood (graph theory)|neighborhood]] is a 4- or 5-vertex cycle.