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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 polyhedra, including the five regular convex polyhedra, five polyhedral compounds, four Kepler-Poinsot polyhedra, and thirteen Archimedean solids, constructing or collecting polyhedron models has become a common mathematical recreation. Polyhedron models are found in mathematics classrooms much as
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, from a single sheet of cardboard. Choosing colours requires geometric understanding of the polyhedron. One way is to colour each 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 five colours, respectively.
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 ''
Stella: Polyhedron Navigator
Software to explore virtual polyhedra and print their nets to enable physical construction
Wooden Polyhedra Models
Online rotatable polyhedron models
Recreational mathematics Model
globe
A globe is a spherical model of Earth, of some other celestial body, or of the celestial sphere. Globes serve purposes similar to maps, but unlike maps, they do not distort the surface that they portray except to scale it down. A model glo ...
s in geography
Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, a ...
classrooms.
Polyhedron models are notable as three-dimensional proof-of-concepts of geometric theories. Some polyhedra also make great centerpieces, tree toppers, Holiday decorations, or symbols. The Merkaba religious symbol, for example, is a stellated octahedron. Constructing large models offer challenges in engineering structural design
Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of man-made structures. Structural engineers also must understand and cal ...
.
Construction
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, from a single sheet of cardboard. Choosing colours requires geometric understanding of the polyhedron. One way is to colour each 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 five colours, respectively.
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 ''Polyhedron Models
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.
A convex polyhedron is the convex hull of finitely many points, not all on t ...
'', 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 edges. The exposed nets of the faces are then traced or printed on template material. A third way is using the software named ''Stella
Stella or STELLA may refer to:
Art, entertainment, and media Comedy
*Stella (comedy group), a comedy troupe consisting of Michael Showalter, Michael Ian Black and David Wain
Characters
*Stella (given name), including a list of characters with th ...
'' to print nets.
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.
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 stellations, can have hundreds of polygons in their nets.
Interactive computer models
Recentcomputer graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great deal ...
technologies allow 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.
See also
* Polyhedron * List of Wenninger polyhedron modelsExternal links
Stella: Polyhedron Navigator
Software to explore virtual polyhedra and print their nets to enable physical construction
Recreational mathematics Model