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# Liste de livres en anglais sur les zomes et dômes

2004, par

Steve Baer, Zome Primer, Zomeworks, 1970

Self-published booklet about the use of zonohedra in an architectural system and the Zometool plastic polyhedral construction toy. (See also Fivefold Symmetry by Hargittai, below.)

T. Bakos, "Octahedra inscribed in a Cube," Mathematical Gazette, Vol. 43, pp. 17-20, 1959.

Describes compounds of 4 cubes and 4 octahedra.

Walter William Rouse Ball, revised by H.S.M. Coxeter, Mathematical Recreations and Essays, New York, 1938 ; 11th ed., 1960, (Dover reprint). ($)

An essential classic of recreational mathematics with a pithy chapter on polyhedra written by Coxeter. This plus many other interesting topics make this an excellent book.

Thomas F. Banchoff, Beyond the Third Dimension : Geometry, Computer Graphics, and Higher Dimensions, W. H. Freeman, 1990.($)

Gentle introduction to polytopes and the geometry of four or more dimensions. Nicely illustrated.

Daniele Barbaro, La Pratica Della Perspettiva, 1569 (Arnaldo Forni reprint, 1980).

Perspective manual with many drawings of polyhedra, including several unusual "symmetrohedra." (in Italian).

Robert Stanley Beard, Patterns in Space, Creative Publications, 1973.

A miscellany of geometric drawings and tables, including polyhedral patterns.

Martin Berman, "Regular-faced Convex Polyhedra," Journal of the Franklin Institute, Vol. 291 No. 5, pp. 329-352, May 1971.

Gives photographs and nets for constructing all of the Johnson solids.

V. G. Boltyanskii, Equivalent and Equidecomposable Figures, Heath 1956.

Discusses the mathematical conditions of when it is possible to dissect a given polyhedron into a finite number of pieces and reassemble them into another given polyhedron.

Max Brückner, Vielecke und Vielflache : Theorie und Geschichte, Teubner, 1900.

Classic turn-of-the-century text (in German) summarizing everything known at the time about polyhedra. Contains drawings, plates, and discussion, including some polyhedral topics not mentioned in the English language literature as far as I know.

M. J. Buerger, Elementary Crystallography, Wiley, 1956, (MIT press reprint, 1978).

Good source for crystallographic polyhedra and the 230 space groups.

Vladimir Bulatov, "An Interactive Creation of Polyhedra Stellations with Various Symmetries," in Proceedings of Bridges : Mathematical Connections in Art, Music, and Science, 2001.

Describes an excellent program for generating stellations.

M. E. Catalan, "Memoire sur la Theorie des Polyedres," Journal de L’ecole Imperiale Polytechnique, Vol. 24, book 41, pp. 1-71 plus plates, 1865.

Original presentation (in French) of the Catalan solids (the duals to the Archimedean solids) plus some combinatorics.

Stewart T. Coffin, The Puzzling World of Polyhedral Dissections, Oxford, 1990. ($)

Great book about wooden take-apart puzzles based on polyhedral shapes, written by a most ingenious puzzle designer. It is available online.

Robert Connelly, "Rigidity," Chapter 1.7 (pp. 223-271) of the Handbook of Convex Geometry, P.M. Gruber and J.M. Wills (editors), Elsevier, 1993.

Mathematical summary of results about the rigidity of polyhedra and tensegrity structures.

Robert Connelly and Allen Back, "Mathematics and Tensegrity," American Scientist, Vol. 86, pp. 142-151, March/April, 1998.

Analysis of polyhedral tensegrity structures.

John Lodge Cowley, Solid Geometry, London, 1752.

Interesting version of Euclid, containing pop-up paper models of polyhedra, including rhombic dodecahedron of 2nd type.

H.S.M. Coxeter, Introduction to Geometry, 2nd ed., Wiley, 1969. ($)

Broad presentation of geometry with sections on platonic solids, the golden ratio, polyhedral symmetry, and four-dimensional polytopes.

H.S.M. Coxeter, The Beauty of Geometry : Twelve Essays, Dover 1999 (reprint, with new title, of Twelve Geometric Essays, S. Illinois U. Pr., 1968). ($)

Collection of mathematical essays ; not elementary.

H.S.M. Coxeter, Kaleidoscopes : Selected Writings of H.S.M. Coxeter, Wiley, 1995. ($)

A collection of Coxeter’s papers, mainly mathematical, on a range of topics, especially polyhedra and polytopes. Also contains a nice biography. (But too expensive !)

H.S.M. Coxeter, Regular Polytopes, Macmillan, 1963, (Dover reprint, 1973). ($) The most outstanding mathematical text on the geometry of polyhedra.

H.S.M. Coxeter, Regular Complex Polytopes, Cambridge, 1974, (2nd ed., 1991). ($) Mathematical text describes a generalization of polyhedra based on complex numbers.

H.S.M. Coxeter, "Virus Macromolecules and Geodesic Domes," in A Spectrum of Mathematics, J.C. Butcher (editor), Aukland, 1971. Analysis of the icosahedron-based forms of various geodesic domes and viruses.

H.S.M. Coxeter, M.S. Longuet-Higgins, and J.C.P. Miller, "Uniform Polyhedra," Philosophical Transactions of the Royal Society, Ser. A, 246, pp. 401-449, 1953.

The first complete list of the uniform polyhedra. The essential mathematical paper on the nonconvex uniform polyhedra.

H.S.M. Coxeter, P. DuVal, H.T. Flather, and J.F. Petrie, The Fifty-Nine Icosahedra, U. Toronto Pr., 1938, (Springer-Verlag reprint, 1982), (Tarquin reprint 1999). ($)

Classic enumeration of the 59 stellations of the icosahedron, with figures and historical notes. The 1999 edition is updated with new diagrams plus photos of some of Flather’s original paper models.

H.S.M. Coxeter, M. Emmer, R. Penrose, and M.L. Teuber (editors), M.C. Escher : Art and Science, North-Holland, 1986.

Collection of papers on Escher’s work, with analyses of his use of tessellations and polyhedra.

K. Critchlow, Order in Space : a design source book, Viking, 1970. ($)

Polyhedra, space-fillers, tessellations, sphere packings, and their relationships, with lots of line drawings.

Peter R. Cromwell, Polyhedra, Cambridge, 1997. ($)

A must-see for anyone interested in polyhedra. Much art, history, and math, in a well illustrated book with lots of nice touches. At 450 pages, with many references, this is by far the most comprehensive book on polyhedra yet printed.

Akos Csaszar, "A polyhedron without diagonals", Acta Univ Szegendiensis, Acta Scient. Math, v. 13, pp 140-2, 1949.

Describes the Csaszar polyhedron : fourteen triangular faces forming a torus.

H. Martyn Cundy and A.P. Rollett, Mathematical Models, Oxford, 1961 ; third edition Tarquin publ., 1981.

An outstanding classic. (I think I had it out from my public library as a youth for two or three years straight.) It has instructions for making many models including Archimedeans, duals, some compounds, some stellations, and two non-convex quasi-regular polyhedra and their duals. Plus plenty of good stuff other than polyhedra.

H. Martyn Cundy and Magnus J. Wenninger, "A compound of five dodecahedra," Mathematical Gazette, pp. 216-218., 1976.

Describes the compound of five dodecahedra.

Margaret Daly Davis, Piero della Francesca’s Mathematical Treatices : The "Trattato d’abaco" and "Libellus de quinque corporibus regularibus," Longo Editore,1977.

Traces the effects of Piero’s writings on renaissance polyhedral developments.

Rene Descartes, De Solidorum Elementis, circa 1637.

See Federico, below.

Andreas W. M. Dress, "A combinatorial theory of Grunbaum’s new regular polyhedra," Aequationes Mathematicae, "Part I," Vol. 23, pp. 252-265, (1981) ; "Part II," Vol. 29, pp. 222-243, (1985).

Two-part article analyzing and enumerating "hollow-faced" regular polyhedra.

Albrecht Durer, Underweysung der Messung,1525,(translated to English as Painter’s Manual, Abaris reprint, 1977).

The earliest use of nets to represent polyhedra.

John D. Ede, "Rhombic Triacontahedra," Mathematical Gazette, Vol. 42, pp. 98-100, 1958.

Discusses the stellation of the rhombic triacontahedron.

Aniela Ehrenfeucht, The Cube Made Interesting, Macmillan, 1964.

Uses 3D line drawings (via a pair of red/blue "3D glasses") to illustrate the symmetries of the cube, its relations to other polyhedra, some dissections, and how to pass a cube through another cube.

Michele Emmer (editor), The Visual Mind, MIT, 1993.

An assortment of interesting papers by various authors on geometry and art, with some polyhedral topics, including one, "Art and Mathematics : The Platonic Solids" by Emmer.

David Eppstein, "Zonohedra and Zonotopes," Mathematica in Education and Research, Vol 5, No. 4, pp. 15-21, 1996.

Mathematica code for generating zonohedra.

M.C. Escher, The Graphic Work of M.C. Escher, Ballantine, 1971.

Art of Maurits Cornelis Escher with his own commentary.

M.C. Escher, Bruno Ernst, The Magic Mirror of M.C. Escher, Ballantine, 1976, (Tarquin reprint, 1982). ($)

Art of Maurits Cornelis Escher with commentary by Ernst on Escher’s life and art, including several pages on his use of polyhedra.

Euclid, The Thirteen Books of the Elements, circa 300 BC, (Dover reprint in three volumes, Thomas L. Heath editor, 1956). ($)

The urtext. Just do it.

P.J. Federico, Descartes on Polyhedra : A Study of the De Solidorum Elementis, Springer-Verlag, 1982. ($)

Translation and analysis of Descartes’ 1637 book which includes his famous angle deficit theorem.

E. S. Fedorov, Symmetry of Crystals, transl. David and Katherine Harker, American Crystallographic Assoc. reprint 1971.

Description of zonohedra and their properties.

J. V. Field, "Rediscovering the Archimedean Polyhedra : Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Durer, Daniele Barbaro, and Johannes Kepler," Archive for History of Exact Sciences, vol. 50, no. 3, pp. 241-289, 1996.

Renaissance history of the rediscovery of the Archimedean polyhedra.

G. M. Fleurent, "Symmetry and Polyhedral Stellation I," Computers Math. Applic., Vol 17, p. 167-175, 1989.

Stellates the chiral icositetrahedron.

Lorraine L. Foster, Archimedean and Archimedean Dual Polyhedra, VHS video tape, 47 minutes, California State University, Northridge, Instructional Media Center, 1990.

Video describing the Platonic and Archimedean solids and their duals, showing many models, some computer animations, and a few mineral crystals, with a section of historical perspective.

Greg N. Frederickson, Dissections : Plane and Fancy, Cambridge, 1997.

Methods of dissecting shapes and reassembling the pieces into other shapes, with three chapters on dissecting polyhedra.

H. Fruedenthal and B.L.van der Waerden, "Over een Bewering van Euclides", Simon Stevin, vol. 25, pp. 114-121, 1947.

Describes the convex equilateral deltahedra. (in Dutch)

Tomoko Fuse, Unit Origami : Multidimensional Transformations, Japan Publications, 1990. ($)

Impressive assemblage of modular origami polyhedra, with photos and instructions.

J. Francois Gabriel (editor), Beyond the Cube : The Architecture of Space Frames and Polyhedra, Wiley, 1997. ($)

Collection of sixteen articles by architects on applications of polyhedra in architecture. (See Hanaor, Tomlow)

Martin Gardner, The Five Platonic Solids, Chapter 1 of his The 2nd Scientific American Book of Mathematical Puzzles and Diversions, Simon and Schuster, 1961.

Some polyhedral puzzles and miscellany.

Matila Ghyka, The Geometry of Art and Life, Sheed and Ward, 1946, (Dover reprint, 1977).

Discusses the relations between polyhedra and art, stretching things a bit far in places.

J. R. Gott, "Pseudopolyhedrons," American Mathematical Monthly, Vol 74, p. 497, 1967.

Illustrates a number of infinite polyhedra constructed of regular polygons.

Ugo Adriano Graziotti, Polyhedra : The Realm of Geometric Beauty, self-published, 1962.

Curious, nicely illustrated, 38 page booklet with original constructions for the Archimedean duals. Watch for errors.

Robert Grip, Tensegrity : Introductory Theory and Model Construction, Fuller, 1978.

Brief, well illustrated, 18 page booklet.

Branko Grunbaum, Convex Polytopes, Interscience, 1967.

Mathematical text focusing on combinatorial issues.

Branko Grunbaum, "Regular Polyhedra --- Old and New," Aequationes Mathematicae, Vol 15, pp. 118-120, 1977.

Short note pointing out that a consistent set of definitions allows for more regular polyhedra than are standardly counted.

Branko Grunbaum, "Polyhedra with hollow faces," in T. Bisztriczky (ed.) Polytopes : Abstract, Convex and Computational, Kluwer, 1994, pp. 43-70.

Detailed framework for a general notion of polyhedra in which the faces are basically a path of edges, and so may be nonplanar, or the edges may go around more than once, or may be infinite, e.g., a helix.

Branko Grunbaum and G. C. Shephard, "Duality of Polyhedra," in Senechal and Fleck (eds.) Shaping Space, Birkhauser, 1988.

Mathematical paper discusses subtle inconsistencies in naive notions of duality.

Rona Gurkewitz, Bennet Arnstein, 3-D Geometric Origami : Modular Polyhedra, Dover, 1995. ($)

An illustrated, step-by-step, how-to-fold-and-construct guide.

Ernst Haeckel, Art Forms in Nature, 1904, Dover reprint, 1974. ($)

Not about polyhedra, but a beautiful book with 100 plates by Haeckel, starting with an icosahedral radiolarian.

Ariel Hanaor, "Tensegrity : Theory and Application," in Gabriel, Beyond the Cube,1997.

Discusses a variety of tensegrity structures, including single and double layer polyhedral forms.

Zvi Har’El, "Uniform Solution for Uniform Polyhedra," Geometriae Dedicata 47, 1993.

Mathematical description of an algorithm (used here) for computing the descriptions of the uniform polyhedra. J. Wenninger, Spherical Models, Cambridge, 1979, (1999 Dover reprint).

Instructions for constructing spherical models based on polyhedral symmetries. Dover version has new additions in an appendix.

Magnus J. Wenninger, Dual Models, Cambridge, 1983.

In the same informative how-to spirit as the above three books, this is the only reference I know which discusses and illustrates the duals to all of the uniform polyhedra.

Magnus J. Wenninger and Peter W. Messer, "Patterns on the Spherical Surface," International Journal of Space Structures, Vol. 11, pp. 183-192, 1996.

Several spherical paper sculptures (with polyhedral symmetry) and how they are designed.

Magnus J. Wenninger, "Polyhedra and the Golden Number," Symmetry, Vol. 1, No. 1, pp. 37-40, 1990.

Shows the "Theosophical" compound of five cubes (which has octahedral symmetry) and one (slightly distorted) compound of ten cubes.

Magnus J. Wenninger, "Some Interesting Octahedral Compounds," Mathematical Gazette, pp. 16-23, Feb., 1968.

Illustrates the compound of three octahedra and a related compound of four.

Hermann Weyl, Symmetry, Princeton U. Pr., 1952.

Classic treatment of symmetry in its many forms, as found in art, nature, and mathematics.

Robert Williams, Natural Structure : Toward a Form Language, Eudaemon Pr., 1972. Reprinted with corrections as The Geometrical Foundation of Natural Structure : A Source Book of Design, Dover, 1979.

An original exploration of design principles using polyhedral structures.

Makoto Yamaguchi, Kusudama : Ball Origami, Shufunotomo, Tokyo, 1990.

Clear instructions for making beautiful modular origami orbs with polyhedral symmetries.

Shukichi Yamana, "An Easily Constructed Dodecahedron Model," Journal of Chemical Education, Vol 61, pp. 1058-1059,1984.

Absolutely, positively, without a doubt, the most difficult method of constructing a dodecahedron I have ever seen in my life. One of the 34 steps is : "Oblique lines are drawn to shade ten equilateral triangles (1P2, 3Q4, 5R6, 7S8, and 9T10 on the right moiety, and 11W12, 13M*14, 3*X15, 16R*S*, and N6*17 on the left moiety)."

V.A. Zalgaller, Convex Polyhedra with Regular Faces, Consultants Bureau, 1969.

A lengthy fastidious mathematical proof that Johnson’s list of solids is complete. Has anyone ever really read this ?

Gunter M. Ziegler, Lectures on Polytopes, Springer-Verlag, 1995.

Excellent mathematical text on convex polyhedra and polytopes.

Douglas Zongker and George W. Hart, "Blending Polyhedra with Overlays," Proceedings of Bridges : Mathematical Connections in Art, Music, and Science, 2001, pp. 167-174.

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