Polyhedron model

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 solids, and thirteen Archimedean solids, constructing or collecting polyhedron models has become a common mathematical recreation. Polyhedron models are found in mathematics classrooms much as globes in geography classrooms.

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 from folding a pattern on 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 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, an 20-face icosahedron can use twenty colours, one colour, ten colours or five colours, respectively.

Templates are then made. One way is to copy templates from a polyhedron-making book. A second way is drawing faces on paper or on computer-aided design software and then drawing on them the polyhedron's edges. The exposed sections of the faces are then traced or printed on template material.

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.

The templates are then replicated unto the material, matching carefully the chosen colours.

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.

See also

• Polyhedron