By Marjorie Senechal
First Steps -- advent to the Polyhedron country / Marjorie Senechal -- Six Recipes for Making Polyhedra / Marion Walter, Jean Pedersen, Magnus Wenninger, Doris Schattschneider, Arthur L. Loeb -- usual and Semiregular Polyhedra / H. S. M. Coxeter -- Milestones within the historical past of Polyhedra / Joseph Malkevitch -- Polyhedra: Surfaces or Solids? / Arthur L. Loeb -- Dürer's challenge / Joseph O'Rourke -- Polyhedra in Nature and artwork -- Exploring the Polyhedron nation / Marjorie Senechal -- Spatial conception and Creativity / Janos Baracs -- Goldberg Polyhedra / George Hart -- Polyhedra and Crystal constructions / Chung Chieh -- Polyhedral Molecular Geometries / Magdolna Hargittai, Istvan Hargittai -- shape, functionality, and Functioning / George Fleck -- Polyhedra within the Geometrical mind's eye -- The Polyhedron state the following day / Marjorie Senechal -- Paneled and Molecular Polyhedra: How sturdy Are They? / Ileana Streinu -- Duality of Polyhedra / Branko Grünbaum, G. C. Shephard -- Combinatorial Prototiles / Egon Schulte -- Polyhedra Analogues of the Platonic Solids / Jörg M. Wills -- Convex Polyhedra, Dirichlet Tessellations, and Spider Webs / Walter Whiteley, Peter F. Ash, Ethan Bolker, Henry Crapo -- Uniform Polyhedra from Diophantine Equations / Barry Monson -- Torus Decompostions of standard Polytopes in 4-space / Thomas F. Banchoff -- Tensegrities and international tension / Robert Connelly -- Ten difficulties in Geometry / Moritz W. Schmitt, Günter M. Ziegler
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Extra resources for Shaping space : exploring polyhedra in nature, art, and the geometrical imagination
A a A b be necessary, so experiment to find the best arrangement. 7. Remove the paper clips when you have a satisfactory arrangement of rubber bands. 8. To flatten the model put your fingers inside and pull at the vertices nearest A and D so that you are pulling those opposite faces away from each other until each is folded along an altitude of that triangular face. 24b. 9. Holding the triangular flaps flat, toss the model and watch it pop up. Just as with the cube, this model will make more noise if you glue an extra triangle on the exposed faces.
They can be seen in the British Museum, although there is some doubt about their exact date. All the five so-called Platonic solids are described in the later books of Euclid. Subsequent writers have made it much easier to see that the number of Platonic solids is just five. First of all, perhaps one should define what one means by a regular solid. It is rather strange that not many people realize how very simple the definition can be. If one starts in the plane defining a regular polygon, one cay say that a polygon is regular if it has a circumcircle and an incircle which are concentric.
You can lay out a tessellated network of such triangles by marking the back or waxy side of a sheet of glitter film with a scoring instrument and then cutting out the triangles with scissors. Next peel off one corner of the waxy backing from the film and attach this to a piece of index card. Finally, remove the entire backing while you smooth out the film on the card. Now trim the card with scissors, leaving a border of card all around the film. A quarter inch or so is suitable (about 7 or 8 mm).