Symmetry: Culture and Science

EDITORIAL 5

SYMMETRY: SCIENCE AND ART

■ Memoirs of a polyhedronist, Magnus J. Wenninger 7
■ Stellated dodecahedron, Vladimir Bulatov 16
■ In the palm of Leonardo's hand: Modeling polyhedra, George W. Hart 17
■ Higher-dimensional zonotopes, Satoshi Yamaguchi 26
■ Octahedrites, Michel Deza and Mikhail Shtogrin 27
■ Symmetrical projections of the high-dimensional regular polytopes,
Carlo H. Séquin 65
■ Occurrence of crystal forms in the central projections of
4-dimensional polytopes, Gábor Gévay and Koji Miyazaki 85
■ Kaleidoscopic polyhdera and tilings, Jeff Weeks 117
■ From the periodic system of Platonic and Archimedean solids and
tessellations to the 4D regular polyhedra and tessellations
(with extension to some 5D polytopes), Szaniszló Bérczi 125
■ Convex segmentochora, Richard Klitzing 139
■ A color-matching dissection of the rhombic enneacontahedron,
George W. Hart 183
■ Stellations of the rhombic triacontahedron and beyond,
Peter W. Messer 201
■ Stella: Polyhedron navigator, Robert Webb 231
■ Towards stellating the icosahedron and faceting the dodecahedron:
New findings on stellation, faceting and untidy polyhedra, Guy Inchbald 269
■ Rhombic spirallohedra, Russell Towle 293
■ The Spidron model, Dániel Erdély 307
■ On three classes of regular toroids, Lajos Szilassi 317
■ Golden rhombic polyhedra, Izidor Hafner 337
■ Crystallography of a space station, Part I:
How to build stellated rhombic triacontahdedral structures from golden
rhombohedra by folding and docking, Sándor Kabai and Szaniszló Bérczi 361
■ The Pythagopod, Christopher Glass 379
■ Multiple unit constructions of face-connected regular dodecahedra:
A comparative study of simple and complex forms, Stephan Werbeck 393
■ Tangrams and Amish quilts, Jay Kappraff 405
■ Rethinking polyhedra: It’s all about transformation, Robert A. Wiggs 425
■ The morphological bridge bridge between logic and aesthetic sensitivity:
The design of a geometry exhibit for the Buenos Aires Science Museum,
Alfredo Cattan, Liliana D’Angeli and Pedro D. Reissig 443

SYMMETRY IN EDUCATION

■ Abstract construction projects and the imagination: Hands-on projects
for understanding abstract mathematical concepts through the use of
poyhedral models and planar designs, Raymond F. Tennant 455

SYMMETRO-GRAPHY

■ Book review 473
■ Marsden, Jerrold E., Ratiu, Tudor S., Introduction to Mechanics
and Symmetry; A Basic Exposition of Classical Mechanical Systems
■ Johnson, D. L., Symmetries
■ Kabai, Sándor, Mathematical Graphics I; Lessons in computer Graphics
Using Mathematica
■ Kinsey, L. Christine, Moore, Teresa, E., Symmetry, Shape, and Space;
An Introduction to Mathematics Through Geometry
■ Hargittai, István and Laurent, Torwald C., eds., Symmetry 2000