Triaugmented triangular prism: Difference between revisions

Revision as of 03:30, 7 July 2023

Revision as of 05:47, 7 July 2023

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==Dual associahedron==

[[File:EnneahedronAssociahedron.pnggif|thumb|Dual polyhedron of the triaugmented triangular prism]]

The [[dual polyhedron]] of the triaugmented triangular prism has a face for each vertex of the triaugmented triangular prism, and a vertex for each face. It is an [[enneahedron]] (that is, a nine-sided polyhedron){{r|fr07}} that can be realized with three non-adjacent [[Square (geometry)|square]] faces, and six more faces that are congruent irregular [[pentagon]]s.{{r|as18}} It is also known as an order-5 [[associahedron]], a polyhedron whose vertices represent the 14 triangulations of a [[regular hexagon]].{{r|fr07}} A less-symmetric form of this dual polyhedron, obtained by slicing a [[truncated octahedron]] into four congruent quarters by two planes that perpendicularly bisect two parallel families of its edges, is a [[space-filling polyhedron]].{{r|goldberg}}