Contents Introduction The Five Platonic Solids The Thirteen Archimedean Solids Prisms, Antiprisms, and Other Polyhedra The Four Kepler-Poinsot Solids Other Stellations or Compounds Some Other Uniform Polyhedra Conclusion Notes Bibliography

Polyhedron Models for the Classroom by Magnus J. Wenninger

Conclusion

Does the construction of polyhedron models have any practical significance apart from the hobby value it undoubtedly possesses? To answer this question, you may refer to Coxeter’s book Regular Polytopes. To quote Coxeter: “The chief reason for studying regular polyhedra is still the same as in the time of the Pythagoreans, namely, that their symmetrical shapes appeal to one’s artistic sense.”⁸ Again: “Anyone who believes that mathematics should be useful as well as beautiful should remember that polytopes have applications not only to the geometry of numbers but also to such practical subjects as the theory of communications and linear programming.”⁹

In a geometry classroom polyhedron models may be used to illustrate the ideas of symmetry, reflection, rotation, and translation. Felix Klein, as far back as 1884, gave lectures on the regular solids and the theory of groups. His lectures on the icosahedron have thrown new light on the general quintic equation.¹⁰ The various color arrangements suggested in this monograph might well be subjected to the mathematical analysis of group theory. At any rate, there is plenty of pure mathematics in the theory of polyhedra. More research may yet yield applications that up to now have never been thought possible.

Polyhedron Models for the Classroom by Magnus J. Wenninger

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		© Ragnar Torfason 2006 June 3