Pavilion of Polyhedreality (original) (raw)

By George W. Hart

I welcome you to peek into my personal pavilion of practical polyhedra. All images are copyright by George W. Hart.

This figure shows me and a tensegrity structure made from coffee stirrers and dacron thread. No two sticks actually touch each other.

Note: For your maximal synesthetic enjoyment, I have chosen short musical selections to go with each picture. If your web viewer isset up to play MIDI music files, just click on any of the red notes before selecting a picture, and you can listen to a J.S. Bach piece as background music while each image is transferring.

The following images are available at the moment:

• Nailbanger's Nightmare A simple project for all you weekend carpenters. Get out those old two-by-four scraps you have been saving. [185K]
• Paper Ball Paper constructions of this sort are amazingly light and strong. There are lots of examples in Wenninger's book Spherical Models, listed below. This one is made of 3120 curved arcs. Geodesic buffs will notice the lack of alignment along the 5-fold axes of symmetry. [82K]
• Puzzle The first part of the puzzle is to figure out the name of the underlying polyhedron, comprising 12 pentagons and 60 hexagons. [250K]
• If you build it, he will come... If you are like me, you like to make things out of paper clips. But the snub dodecahedron is a relatively tough one, though not impossible. At each vertex, one pentagon and four equilateral triangles meet. [104K]
• Selected Recent Publications This may be a reaction to unpleasant academic experiences. [179K]
• Apples and Oranges If you like to play with your food and silverware, I am sure you make little dinner-time sculptures as I do. Here, sixty forks, arranged along the edges of a rhombic triacontahedron, bind 12 apples (placed at the corners of an icosahedron) and 20 oranges (placed at the corners of a dodecahedron). [243K]
• Artificial Radiolarian ReticulumRadiolarians are microscopic ocean-living protozoa with complex geodesicly-perforated silica skeletons and sharp spicules. Drawings of a great variety of Radiolaria skeletons by the 19th century naturalist Ernst Haeckel can be found in many books that deal with geometry, symmetry, and nature. This image attempts to capture the idea of a radiolarian and is not faithful to any particular species. [214K] The above figures were each ray traced with POV-ray, using data files produced by a polyhedral construction program I wrote which creates a wide variety of objects with icosadodecahedral symmetry. The program is described in this paper.
• Stained Glass Ball This is just a concept (not raytraced) based on the zonohedrification of the rhombic enneacontahedron. Exactly 1230 pieces of glass are required. [47K]

--- Virtual Reality Polyhedra ---

To learn more than you ever wanted to know about polyhedra, you will want to visit my Encyclopedia of Polyhedra. It is intended as a museum of objects, a reference work, and a tutorial of sorts, all dedicated to the serene, timeless beauty of polyhedra and their interrelationships. Over 1000 polyhedra are on display here --- from the familiar to the never-before-seen --- far more than have ever been assembled or collected anywhere. All are truly three-dimensional, meaning you can rotate them and move them around on your computer screen. I plan to complete and publish the Encyclopedia someday as a combination book and CD ROM. In the meantime, you are welcome to take a look as I write each new section.

Other Sites...

Here are a few other web pages related to polyhedral and/or geodesic stuff:

• My Virtual Polyhedra (see above)
• My sculpture gallery
• My annotated bibliography of polyhedra references
• Zometool --- my favorite polyhedron construction set (my zometool page)
• Jill Britton's page of polyhedra links
• Magnus Wenninger's home page
• Ulrich Mikloweit's incredible paper models
• Vladimir Bulatov's raytraced and VRML polyhedra
• Kris Manske's polyhedra pages
• Roman Maeder's uniform polyhedra Pages
• Tom Gettys' polyhedra Pages
• Ha Quang Le's VRML polyhedra and Maple code
• Mike Rollins' Polyhedra in Light Bulbs
• Junichi Yananose's puzzles and VRML constructions
• Jim McNeill's VRML polyhedra
• Henry Chasey's polyhedra model collection
• Jan de Koning's wooden polyhedra models
• Bob Allanson's polyhedra pages and polyhedron generator
• Scott Vorthman's Zomeworks software
• Edwin Otoole's ring kits
• Rolf Asmund's polyhedra pages
• Steve Dutch's polyhedra pages
• Tom York's polyhedron program
• Daniel B. Grunberg's _Poly_program
• Izidor Hafner's visualization olympiad and rhombic polyhedra
• Mike Eisenberg and Ann Nishioka's HyperGami
• George Olshevsky's paper models and polytope page
• Polydron --- a snap-together polygon construction set
• Polymorf --- another, but which allows more than two faces per edge
• Peter Cromwell's Polyhedra book
• Tom Lechner's polyhedra
• Anthony Thyssen's giant polyhedral kites
• Stewart T. Coffin's Puzzling World of Polyhedral Dissections
• Greg Egin's polyhedral (and other) applets
• VRML crystal structures at the Institut Laue - Langevin
• dForm's VRML constructions of Platonic polyhedra
• Farideh Dormishian and Rudy Rucker's Hypercube 98
• Lexington High School's World's Largest Icosahedron
• Kenneth Snelson's tensegrity structures
• Leigh Boileau's wire models
• Tom Longtin's Polyhedral (and other) images
• Mark's Newbold's stereoscopic animated hyperspace objects
• Pan Dragon's polyhedral animations
• Daniel Green's geometry pages
• Sam Gratrix's ray-traced polyhedra
• Robert Dawson's ray-traced polyhedra
• Mathematica Graphics Gallery
• Stewart Dickson's Polyhedral Constructions
• Steffan Scheller's polyhedral stuff
• Doug Zongker's Polyhedral templates
• Bathsheba Grossman's geometric sculptures
• David Eppstein's Geometry Junkyard
• Stephan Werbeck's dodecahedron constructions
• Dave Rusin's notes on polyhedra
• Gordon Kindlmann's peek at polytope slices
• Laurens Lapré's polyhedra images
• Martin Trump's random polyhedra pictures
• Philo's Polyhedral Panoramic Photos
• Rona Gurkewitz's Modular Origami Polyhedra
• Jim Plank's Origami Page
• Tom Hull's Modular Origami
• Krystyna Burczyk's Modular Origami
• Meenakshi's Modular Origami
• Matt Holland's modular origami
• John Sharp's Sliceform models
• Jack Snoeyink's Un-disassemble-able Object.
• Kirby Urner's Synergetics Home Page.
• Steve Waterman's polyhedra with lattice-point vertices
• The group for hyperspace
• The Geometry Center
• The Geometry Forum
• Linda Stannard's Principles of Virus Structure
• Icosahedral Virus Images (U. Wisconsin)
• Buckminster Fuller FAQ
• Paul Flavin's Polyhedra viewer
• Richard Hawkins' Synergetic Geometry
• Bill Collins's Tensegrity Structure Gallery
• Uxbridge High School's stained glass truncated icosahedron
• 2000 polyhedra at Wallsend Central Middle School
• Vedder Wright's Forksphere
• NetLib database
• Zvi Har'El's Kaleido Program
• Good Construction advice (J. Conway)
• Glitter Globe (pentakis dodecahedron circuit kit) Here are some interesting and/or popular illustrated references on polyhedra. For a substantial annotated bibliography, see the annotated bibliography of references in Virtual Polyhedra.
• George W. Hart and Henri Picciotto, Hands-on Geometry with the Zome System, Key Curriculum Press.
• Anything by H.S.M. Coxeter.
• Peter R. Cromwell, Polyhedra, Cambridge, 1997.
• H. Martyn Cundy and A.P. Rollett, Mathematical Models, Oxford, 1961.
• Alan Holden, Shapes, Spaces and Symmetry, Columbia Univ. Pr, 1971.
• Peter Pearce, Structure in Nature is a Strategy for Design, MIT, 1978.
• Anthony Pugh, Polyhedra: A Visual Approach, U. Cal. pr., 1976.
• Marjorie Senechal and George Fleck (eds.), Shaping Space: A Polyhedral Approach, Birkhauser, 1988.
• Magnus J. Wenninger, Polyhedron Models, Cambridge, 1971.
• Tarquin Books of polyhedra models In addition, though it is not directly related to polyhedra, if you are interested in applied mathematics and linear algebra, you will of course want to check out my book, Multidimensional Analysis.

Comments by email to george@georgehart.comare welcome.

And for those of you who are wondering: Yes, "Polyhedreality" is a hapax legomenon.