The Pavilion of Polyhedreality
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
and dacron thread. No two sticks actually touch each other.
Note: For your maximal synesthetic enjoyment, I have
short musical selections to go with each picture. If your web viewer is
up to play MIDI music files, just click on any of the red notes
selecting a picture, and you can listen to a J.S. Bach piece as
music while each image is transferring.
The following images are available at the moment:
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
The program is described in this
- Nailbanger's Nightmare A simple project
you weekend carpenters. Get out those old two-by-four scraps you have
- Paper Ball Paper constructions of
are amazingly light and strong. There are lots of examples in
book Spherical Models, listed below. This one is made of 3120
arcs. Geodesic buffs will notice the lack of alignment along the 5-fold
axes of symmetry. [82K]
- Puzzle The first part of the puzzle
out the name of the underlying polyhedron, comprising 12 pentagons and
60 hexagons. [250K]
- If you build it, he will come... If
like me, you like to make things out of paper clips. But the snub
is a relatively tough one, though not impossible. At each vertex, one
and four equilateral triangles meet. [104K]
- Selected Recent Publications This may
to unpleasant academic experiences. [179K]
- Apples and Oranges If you like to
your food and silverware, I am sure you make little dinner-time
as I do. Here, sixty forks, arranged along the edges of a rhombic
bind 12 apples (placed at the corners of an icosahedron) and 20 oranges
(placed at the corners of a dodecahedron). [243K]
- Artificial Radiolarian Reticulum
are microscopic ocean-living protozoa with complex
silica skeletons and sharp spicules. Drawings of a great variety of
skeletons by the 19th century naturalist Ernst Haeckel can be found in
many books that deal with geometry, symmetry, and nature. This image
to capture the idea of a radiolarian and is not faithful to any
- Stained Glass Ball This is
(not raytraced) based on the zonohedrification of the rhombic
Exactly 1230 pieces of glass are required. [47K]
--- Virtual Reality Polyhedra ---
To learn more than you ever wanted to know about polyhedra, you will
to visit my Encyclopedia of
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 ---
the familiar to the never-before-seen --- far more than have ever been
assembled or collected anywhere. All are truly three-dimensional,
you can rotate them and move them around on your computer screen. I
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.
are a few other web pages related to polyhedral and/or geodesic stuff:
Here are some interesting and/or popular illustrated references on
For a substantial annotated bibliography, see the annotated
bibliography of references in Virtual
In addition, though it is not directly related to polyhedra, if you are
interested in applied mathematics and linear algebra, you will of
want to check out my book, Multidimensional
- George W. Hart and Henri
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,
- Alan Holden, Shapes, Spaces and Symmetry, Columbia Univ.
- Peter Pearce, Structure in Nature is a Strategy for Design,
- Anthony Pugh, Polyhedra: A Visual Approach, U. Cal. pr.,
- Marjorie Senechal and George Fleck (eds.), Shaping Space: A
Approach, Birkhauser, 1988.
- Magnus J. Wenninger, Polyhedron Models, Cambridge, 1971.
- Tarquin Books of polyhedra models
Comments by email to firstname.lastname@example.org
And for those of you who are wondering: Yes, "Polyhedreality" is a