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{{for|the compiler optimization|Polytope model}}
[[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]].
==
[[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 second decision involves colours.
▲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''.
:For example, a 20-face [[icosahedron]] can use twenty colours, one colour, ten colours, or five colours, respectively.▼
▲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 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]].
An
▲:For example, a 20-face [[icosahedron]] can use twenty colours, one colour, ten colours or five colours, respectively.
Net templates are then made.
▲An alternate way for [[polyhedral compound]] models is to use a different colour for each polyhedron component.
A model, particularly a large one, may require another polyhedron as its inner structure or as a construction mold.
▲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]]'', [[1974]] (ISBN 0-521-09859-9). A second way is drawing faces on paper or with [[computer-aided design]] software and then drawing on them the polyhedron's [[edge]]s. The exposed nets of the faces are then traced or printed on template material. A third way is using the software named ''[[Stella (software)|Stella]]'' to print nets.
The net templates are then replicated onto the material, matching carefully the chosen colours. Cardboard nets are usually cut with tabs on each edge, so the next step for cardboard nets is to score each fold with a knife.
▲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.
Assembling multi-colour models is easier with a model of a simpler related polyhedron used as a colour guide.
▲The net templates are then replicated onto the material, matching carefully the chosen colours. Cardboard nets are usually cut with tabs on each edge, so the next step for cardboard nets is to score each fold with a knife. Panelboard nets, on the other hand, require molds and cement adhesives.
▲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 or over a thousand polygons in their nets.
Recent [[computer graphics]] technologies
==
*[[List of Wenninger polyhedron models]]
*[http://web.aanet.com.au/robertw/Stella.html Stella: Polyhedron Navigator] - Software to generate and printing nets for polyhedra ▼
▲== Interactive computer models ==
▲Recent [[computer graphics]] technologies allowed people to rotate 3D polyhedron models on a computer video screen in all three dimensions. Recent technologies even provide shadows and textures for a more realistic effect.
▲* [[Polyhedron]]
=== External links ===▼
*[http://ibiblio.org/e-notes/3Dapp/Convex.htm Interactive 3D polyhedra in Java]▼
▲*[http://
▲*[https://web.archive.org/web/20050403235101/http://ibiblio.org/e-notes/3Dapp/Convex.htm Interactive 3D
*[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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