Click here for the Homepage Click here for the Homepage Click here for the Homepage
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

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.
Previous Section Go to the PREVIOUS Section Go to the NEXT Section Next Section

Go to The Renaissance Man's Weeb Page
Click to E-Mail   Ragnar Torfason
2006 June 3