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 Photographs: Stanley Toogood’s International Film Productions, Nassau, Bahamas

Polyhedron Models for the Classroom by Magnus J. Wenninger

Prisms, Antiprisms, and Other Polyhedra
The construction of a few prisms and antiprisms will next give you a good idea of why these belong to the set of semiregular solids. You already have the required nets, since they are the same polygons as those used for the Archimedean solids. A prism has any regular n-gon for end faces and squares for side faces. The antiprism has equilateral triangles instead of squares for side faces. Once you have made some of these, you will find that it is possible for you to branch off on your own into many different types of irregular solids. Some of these come up in textbook problems in a mathematics class: right pyramids (with regular bases or otherwise) having isosceles triangles for sides, various types of oblique pyramids, parallelepipeds, truncated pyramids, and others. You will have noticed that some of the Archimedeans are truncated versions of the Platonic solids. There are some interesting dissection problems in connection with the tetrahedron and the cube. These take on added interest for their usefulness as puzzles. If you are interested in mechanical drawing, you will find that many of the objects you are called upon to draw can also be constructed as models in paper according to the techniques suggested in this monograph. Sections of solids can also be illustrated in this way. In fact, even circular cones and conic sections can be similarly done. (See Figures 9-17 for some suggestions.) Then why not go ahead and discover some others on your own?

Fig. 9, Square pyramid.

Fig. 10, Pentagonal pyramid.

Fig. 11, Three of these form a cube.

Fig. 12, Four of these form a tetrahedron.

Fig. 13, Four of these with a tetrahedron form a cube.

Fig. 14, A closed "box".

Fig. 15, Hexagonal section of a cube. Two of these form a cube.

Fig. 16, Truncated pyramid.

Fig. 17, Circular cone.

Polyhedron Models for the Classroom by Magnus J. Wenninger			Reprinted with permission from Polyhedron Models, copyright 1966 by the National Council of Teachers of Mathematics. All rights reserved.
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		Ragnar Torfason 2006 June 3