Polyhedron model: Difference between revisions

Revision as of 02:50, 16 October 2005

Revision as of 22:17, 10 December 2005

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[[Image:Universiteit_Twente_Mesa_Plus_Escher_ObjectUniversiteit Twente Mesa Plus Escher Object.jpg|thumb|A sculpture of the [[small stellated dodecahedron]] in [[M. C. Escher]]'s ''[[Gravitation (M. C. Escher)|Gravitation]]'', near the Mesa+ Institute of [[Universiteit Twente]]]]

A '''polyhedron model''' is a physical construction of a [[polyhedron]], constructed from cardboard, plastic board, wood board or other panel material, or, less commonly, solid material.

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Construction begins by choosing a ''size'' of the model, either the ''length'' of its edges or the ''height'' of the model. The size will dictate the ''material'', the ''adhesive'' for edges, the ''construction time'' and the ''method of construction''.

The second decision involves colours. A single-colour cardboard model is easiest to construct -- and some models can be made by folding a pattern, a '''[[Net (polyhedron)|net]]''', on a single sheet of cardboard. Choosing colours requires geometric understanding of the polyhedron. One way is to colour each [[Face_%28mathematics%29Face (mathematics)|face]] differently. A second way is to colour all square faces the same, all pentagon faces the same, and so forth. A third way is to colour opposite faces the same. A fourth way is to a different colour each face clockwise a certain [[vertex]].

:For example, a 20-face [[icosahedron]] can use twenty colours, one colour, ten colours or five colours, respectively.

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*[http://ibiblio.org/e-notes/3Dapp/Convex.htm Interactive 3D polyhedra in Java]

[[Category:Recreational_mathematicsRecreational mathematics]]