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 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 globes in geography 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.

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.

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