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revue interdisciplinaire de g&om&rieappliquke aux probl&mesde structure et morphologieen design, architecture et gCnie PARUTION NUMtiRO: ISSUE NUMBER: 10 interdisciplinary journal on geometryapplied to problemsof structure and morphologyin architecture, designand engineering La revue est publiee par le groupe de recherche ‘Topologie The Journal is published by the Structural Topology L’Cquipe de ce numkro / Staff for this issue structurale’, avec la collaboration de I’Association math& research group, with the collaboration of the Association matique du Quebec et de 1’UniversitC du Quebec a mathematique du Quebec and the Universite du Quebec a Montreal. Montreal. Redaction/Editors Henry Crapo Jacques Arc hambault Cornit de direction / Management committee Janos J. Baracs Michel Fleury Walter Whiteley, president et representant du groupe de recherche ‘Topologie structurale’/president and representative of Jean-Luc Raymond the Structural Topology research group, Champlain Regional College, St. Lambert, Quebec. Walter Whi teley Janos J. Baracs, representant de son Ccole/representative of his school, Ecole d’architecture, Universite de Montreal. Traduction/Translation Henry Crapo Henry Crapo, redacteur en chef et membre ex officio/editor in chief and ex officio member, departement de mathemati- Jean-Luc Raymond ques, Universite du Quebec a Montreal. Francine Lefebvre Michel Fleury, reprtsentant de son dCpartement/representative of his department, departement de design, Universite du Jacques Archambault Quebec a Montreal. Typographic/Typesetting Pierre Leroux, representant de son departement/representative of his department, departement de mathematiques, Carole Deslandes UniversitC du Quebec a Montreal. Modulo Editeur Outremon t, Quebec Richard Pallascio, representant de 1’Association mathematique du Quebec/representative of the Association mathemati- que du Quebec, College Edouard-Montpetit, Longueuil, Quebec. Correction des textes/Proof reading Jacques Archambault Cornit consultatif / Advisory board Mise en page/Composition Dominique Lalancette Laszlo Fejes-T&h, mathematician. Professor, Hungarian Academy of Sciences, Budapest, Hungary. Robert Labelle Branko Griinbaum, mathematician. Professor, University of Washington, Seattle, Washington, U.S.A. Photogravure Normand Lacas Lionel March, architect. Director, Centre for Configurational Studies; professor, The Open University, Milton Keynes, England. Impression/Printing Cedric Marsh, engineer. Professor, Centre for Building Studies, Concordia University, Montreal, Quebec. Imprimerie Gag& Louiseville, Quebec Gert Sabidussi, mathematicien. Professeur, UniversitC de Montreal, Montreal, Quebec. Moshe Safdie, architect. Director, Urban Design Program, Graduate School of Design, Harvard University, Cambridge, Massachusetts, U.S.A. @La revue (<Topologie structuraleN>,Universite du Geoffrey Shephard, mathematician. Professor, University of East Anglia, Norwich, England. Quebec a Montreal, 1982. Depot legal: Bibliotheque Nationale, Quebec, 4e trimestre 1984; Bibliotheque Nationale, Ottawa Rklaction / Editors (ISSN 02269171). Henry Crapo, rkdacteur en chef/editor in chief, departement de mathtmatiques, Universite du Quebec a Montreal. Jacques Archambault, directeur administratif/managing editor, departement de mathtmatiques, UniversitC du Quebec 8 Montreal. @La revue (<Topologie structuraleBb, UniversitC du Janos J. Baracs, redacteur/editor, kcole d’architecture, Universite de Montreal. Quebec a Montreal, 1982. Michel Fleury, rCdacteur/editor, departement de design, Universite du Quebec a Montreal. Deposit: Bibliotheque Nationale, Quebec, 4e trimestre 1984; National Library, Ottawa Jean-Luc Raymond, redacteur/editor, departement de mathtmatiques, Universite du Quebec a Montreal. (ISSN 02269171). Walter Whiteley, redacteur/editor, Champlain Regional College, St. Lambert, Quebec. Topologie structurale Structural Topology MO, 1984 #lo, 1984 Table des mat&es Table of Contents Avant-propos 4 Foreword Une introduction a la theorie des figures: la geomttrie de E.S. Fedorov 5 An Introduction to the Theory of Figures: the Geometry of E.S. Fedorov par Marjorie Senechal et R.V. Galiulin by Marjorie Senechal et R.V. Galiulin Compte rendu: La forme de l’espace: polygones, polyedres et polytopes 23 Review: Form of Space: Polygons, Polyhedra and Polytopes par Koji Miyazaki by Koji Miyazaki L’hexagone regulier quadridimensionnel 27 Four-Dimensional Regular Hexagon par Koji Miyazaki by Koji Miyazaki L’art et les mathematiques: une seconde serie de films 35 Art and Mathematics: A Second Series of Movies par Michele Emmer by Michele Emmer La rigidite des reseaux spatiaux composes 41 The Rigidity of Compound Spatial Grids par Alain Dandurand by Alain Dandurand La rigidite generique des graphes biparti-complets dans Rd 57 Generic Rigidity of Complete Bipartite Graphs in Rd par Jean-Luc Raymond by Jean-Luc Raymond Compte rendu sur (Shaping Space)> 63 Report on “Shaping Space” par Janos J. Baracs by Janos J. Baracs Notes aux lecteurs 66 Notes to our Readers Courrier 67 Letters Notes a l’intention des collaborateurs 71 Notes to Contributors Abonnements 72 Subscriptions Remerciements 74 Acknowledgements Avant-propos Foreword La revue Topologie structurale est publiee par le groupe de recherche ‘Topologie structu- The journal Structural Topology is published by the Structural Topology research group, rale’, avec la collaboration de 1’Association mathematique du Quebec et de l’universite du with the collaboration of the Association mathematique du Quebec and the Universite du Quebec a Montreal. Le groupe de recherche est une Cquipe multidisciplinaire composee a Quebec a Montreal. The research group is an interdisciplinary team bringing together la fois de mathtmaticiens, d’ingenieurs, d’architectes, de designers et d’artistes. mathematicians, engineers, architects, designers and artists. Le champ d’interet specifique de la revue est l’application des mathematiques classiques et The particular field of interest of the Journal is the application of classical and contempo- contemporaines (specialement de la geometric) a la solution de problemes morphologi- rary mathematics (especially geometry) to the solution of morphological and structural ques et structuraux qui se posent en architecture et en design. Sesprincipaux themes ont problems arising in architecture and design. The principal themes of this research are trait a l’architecture et sont: les formes polykdriques (modules elementaires), la juxtaposi- questions relevant to construction, namely: polyhedral forms (living units), juxtaposition tion de ces formes (en habitations) et la rigidit des structures resultantes. of these forms (into dwellings) and the rigidity of the resulting structures. Le but de la revue: The aim of the Journal: l rassembler et mettre en communication les chercheurs interesses aux problemes de l to gather together and promote interchange between researchers who are interested in topologie structurale, a un niveau theorique et pratique; the problems of structural topology, at a theoretical or practical level; l publier les resultats recents, les applications recentes et les problemes non resolus dans l to publish recent results, recent applications and unsolved problems in these areas; ces domaines; l to encourage interdisciplinary communication, thereby making the results available to a l encourager la communication interdisciplinaire, par consequent mettre les resultats a la wide audience; disposition d’un large public; l to describe teaching projects and materials which illustrate those themes and which use l decrire les projets et le materiel d’enseignement qui illustrent ces themes et se servent de those results. ces resultats. With these objectives, the Journal contains: Avec ces objectifs, la revue comporte: l longer articles describing recent theoretical advances, current projects and applications l des articles longs decrivant des progres theoriques r&cents, des projets en tours et des in the field of structural topology; applications dans le domaine de la topologie structurale; l brief reports on recent work, including unsolved problems and reviews of work relevant l de brefs rapports sur des travaux recents, incluant des problemes non resolus et des to the themes of structural topology; comptes rendus de travaux lies aux themes de la topologie structurale; l expository articles which describe methods and results in such a way that students and l des articles d’introduction decrivant les methodes et les resultats de facon telle que les practitioners can apply them; etudiants et les gens du metier puissent les appliquer; l popular articles which translate the results into a visual form accessible to a broad l des articles populaires qui traduisent les resultats en une forme visuelle accessible a un audience not familiar with technical mathematics. large public peu familier avec les mathematiques techniques. We invite our readers to send their comments on the Journal and to submit articles for Nos lecteurs sont invites a nous envoyer leurs commentaires sur la revue et a nous publication in forthcoming issues. The editors will make every effort to maintain a soumettre des articles pour publication. La redaction s’efforcera de maintenir un tquilibre balance between theoretical, applied and expository articles, and to develop contacts entre les articles theoriques, appliques et d’introduction, et de developper des contacts between the diverse groups who share an interest in the field of structural topology. entre les divers groupes
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