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[[Image:Universiteit 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.
Since there are 75 [[uniform polyhedron|uniform polyhedra]], including the five [[Platonic solid|regular convex polyhedra]], five [[polyhedral compound]]s, four [[Kepler-Poinsot
Polyhedron models are notable as three-dimensional [[proof-of-concept]]s of geometric theories. Some polyhedra also make great centerpieces, [[tree topper]]s, Holiday decorations, or symbols. The [[Merkaba]] religious symbol, for example, is a [[stellated octahedron]]. Constructing large models offer challenges in engineering [[structural design]].
==Construction==
[[File:Dodecahedron flat.svg|thumb|A net for the regular [[dodecahedron]]]]
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, called a '''[[net (polyhedron)|net]]''', from a single sheet of cardboard. Choosing colours requires geometric understanding of the polyhedron. One way is to colour each [[face (geometry)|face]] differently. A second way is to colour all square faces the same, all pentagonal faces the same, and so forth. A third way is to colour opposite faces the same. Many polyhedra are also coloured such that no same-coloured faces touch each other along an edge or at a vertex.
:For example, a 20-face [[icosahedron]] can use twenty colours, one colour, ten colours, or
An alternative way for [[polyhedral compound]] models is to use a different colour for each polyhedron component.
Net templates are then made. One way is to copy templates from a polyhedron-making book, such as [[Magnus Wenninger]]'s ''[[List of Wenninger polyhedron models|Polyhedron Models]]'',
A model, particularly a large one, may require another polyhedron as its inner structure or as a construction mold. A suitable inner structure prevents the model from collapsing from age or stress.
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Assembling multi-colour models is easier with a model of a simpler related polyhedron used as a colour guide. Complex models, such as [[stellation]]s, can have hundreds of polygons in their nets.
==Interactive computer models==
Recent [[computer graphics]] technologies allow people to rotate 3D polyhedron models on a computer video screen in all three dimensions. Recent technologies even provide shadows and [[texture (computer graphics)|textures]] for a more realistic effect.
==See also==
*[[Polyhedron]]
*[[List of Wenninger polyhedron models]]
*[http://
*[https://web.archive.org/web/20050403235101/http://ibiblio.org/e-notes/3Dapp/Convex.htm Interactive 3D polyhedra in Java]
*[http://bulatov.org/polyhedra/wooden/ Wooden Polyhedra Models]
*[http://www.georgehart.com/virtual-polyhedra/vp.html George Hart's extensive encyclopedia of polyhedra]
*[http://www.georgehart.com/pavilion.html George Hart's Pavilion of Polyhedreality]
*[http://polyhedra.org Online rotatable polyhedron models]
*[http://woodenpolyhedra.web.fc2.com/woodenpolyhedra30.html WOODEN POLYHEDRA 30]
[[Category:Recreational mathematics]]
[[Category:Polyhedra|Model]]
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