The Geometry Junkyard: Models of Polyhedra

Models of Regular Polyhedra

One of the most common forms of geometric model-making involves construction of the five Platonic solids, and of various related symmetric three-dimensional polyhedra. The most common construction methods involve folding and gluing together cut-out paper polygons, but some of these model-builders have carved their polyhedra from solid materials.

Bamboo C.O.R.P.S.. Durable bamboo models of the Platonic and Archimedean polyhedra, offered for sale.
Beezer's PlayDome. Rob Beezer makes truncated icosahedra out of old automobile tires.
Breaking Bonds. Geometric sculpture by Stephen Luecking combining buckyball, hexagon, and amorphous shapes of carbon molecules.
Cardahedra. Business card polyhedral origami.
Andrew Crompton. Grotesque geometry, Tessellations, Lifelike Tilings, Escher style drawings, Dissection Puzzles, Geometrical Graphics, Mathematical Art. Anamorphic Mirrors, Aperiodic tilings, Optical Machines.
Die-cast metal polyhedra available for sale from Pedagoguery Software.
Dodecahedral melon and other fruit polyhedra, by Vi Hart.
Glass dodecahedron. Custom-made for Clive Tooth by Bob Aurelius.
High school buckyball art. Kerry Stefancyk, Allison Cahill, and Jessica Smith make polyhedral models out of stained glass.
Interlocking puzzle pieces and other geometric toys.
Jovo Click 'n Construct. Plastic click-together triangular, square, and pentagonal tiles for building models of polyhedra and polygonal tilings. Includes a mathematical model gallery showing examples of shapes constructable from Jovo.
Landry Art, Escheresque tessellations, and balsa and paper polyhedra, including some prints, t-shirts, and models available for purchase.
Tom Lechner's Sculptures. Lechner makes geometric models from wood, water, plexiglass, and steel.
Materialized Mathematical Models. Jan de Koning exercises his furniture-making skills by making wood, plastic, stone and steel polyhedra.
Modular pie-cosahedron. Turkey Tek makes geometric models out of pecan pie.
Octacube. Stainless steel 3d model of the 24-cell (one of the six regular polytopes in four dimensions), by Adrian Ocneanu, installed as a sculpture in the Penn State Math Department. Includes also a shockwave flythrough of the model.
Origami polyhedra. Jim Plank makes geometric constructions by folding paper squares.
Paperforms. John Vonachen uses laser cutters and spray paint to make and sell paper models of polyhedra, stellated polyhedra, polyhedral complexes, Sierpinski tetrahedra, etc.
The pavilion of polyhedreality. George Hart makes geometric constructions from coffee stirrers and dacron thread. Includes many pointers to related web pages.
Polycell. George Olshevsky makes and sells polyhedra from colored cardstock.
Polyedergarten. Ulrich Mikloweit makes polyhedral models out of colored typewriter paper, cut into lace so you can see the internal structure.
Polyhedra plaited with paper strips, H. B. Meyer. See also Jim Blowers' collection of plaited polyhedra.
Polyhedral solids. Ray-traced images by Tom Gettys, and a primer on constructing paper models.
Polyhedron man. Nice article from Ivars Peterson's Mathland about George Hart and his polyhedral art.
Rhombic triacosiohedron. Pretty model of a nonconvex genus-11 polyhedron with 300 congruent faces.
Rob's polyhedron models, made with the help of his program Stella.
Snub cube and dodecahedron. Rob Moeser makes geometric constructions by carving broccoli stalks.
Stained glass icosidodecahedron and rhombicosidodecahedron, Helen & Liam Striker.
Starpage. Art-deco paper models of stellated polyhedra, by merrill.
30 computers. Forrest McCluer makes polyhedral sculptures out of discarded electronics.
Truncated icosahedral symmetry. Explains why you might want to use a machined aluminum buckyball as a gravity-wave detector...
Truncated Nano-Octahedron. Ned Seeman makes polyhedra out of DNA molecules.
Tune's polyhedron models. Sierpinski octahedra, stellated icosahedra, interlocking zonohedron-dissection puzzles, and more.
270-strut tensegrity sphere. Jim Leftwich makes polyhedra out of dowels and hairbands.
Unfolding polyhedra. A common way of making models of polyhedra is to unfold the faces into a planar pattern, cut the pattern out of paper, and fold it back up. Is this always possible?
Walt's toy box. Walt Venables collects geometric toys, and uses them to help design geodesic domes.
Fr. Magnus Wenninger, OSB, mathematician, builder of polyhedra.
Wooden ball-and-stick models of Archimedean solids, offered for sale by Dr. B's Science Basics.
Wooden polyhedra from Japan (but with English explanations). And more, in Japanese.
The world's largest icosahedron. Jason Rosenfeld makes polyhedra out of ten foot poles and shark fishing line.
Vedder Wright makes geometric models out of plastic forks.

From the Geometry Junkyard, computational and recreational geometry pointers.
Send email if you know of an appropriate page not listed here.
David Eppstein, Theory Group, ICS, UC Irvine.
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