This page describes physical objects
corresponding to geometric constructions (and methods for creating such
See also the origami page, for models made of
folded paper, and the toys page, for some
commercially-available geometric model construction kits.
- Acme Klein Bottle.
A topologist's delight, handcrafted in glass.
fractal and mathematically inspired jewelry.
- Anna's pentomino page. Anna Gardberg makes pentominoes out of sculpey and agate.
- Art, Math,
and Computers -- New Ways of Creating Pleasing Shapes, C. Séquin,
Educator's TECH Exchange, Jan. 1996.
Art and Science of Tiling.
Penrose tiles at Carleton College.
at the 2005 Joint Mathematics Meetings, including many geometric models.
of the Tetrahedron. And by "Art" he means "Arthur". Arthur
Silverman's geometric sculpture, from Ivars Peterson's MathTrek.
- The Atomium, structure formed
for Expo 1958 in the form of nine spheres, representing an iron
crystal. The world's largest cube?
- Belousov's Brew.
A recipe for making spiraling patterns in chemical reactions.
- Constructing Boy's surface out of paper and tape.
- Crocheted Seifert surfaces by Matthew Wright. George Hart, Make Magazine.
circles: theorems in wheat fields. Various hoaxers make geometric
models by trampling plants.
- The downstairs half bath.
Bob Jenkins decorated his bathroom with ceramic and painted pentagonal tiles.
- Escher for real and
Escher for real.
Gershon Elber uses layered manufacturing systems to build 3d models of
Escher's illusions. The trick is to make some seemingly-flat surfaces
curve towards and away from the viewplane.
- Helaman Ferguson mathematical sculpture.
- Fisher Pavers.
A convex heptagon and some squares produce an interesting four-way
symmetric tiling system.
equilateral tori. Can one build a polyhedral torus in which all
faces are equilateral triangles and all vertices have six incident
edges? Probably not but this physical model comes close.
- Fun with Fractals and
the Platonic Solids. Gayla Chandler places models of polyhedra and
polyhedral fractals such as the Sierpinski tetrahedron in scenic outdoor
settings and photographs them there.
geometric models. From the Gaudí museum in
Parc Güell, Barcelona.
- Geometrinity, geometric sculpture by Denny North.
with growth spirals on the basal pinacoids. Pretty pictures of
spirals in crystals. (A pinacoid, it turns out, is a plane parallel to
two crystallographic axes.)
triambic icosidodecahedron quilt,
made by Mark Newbold and Sarah Mylchreest with the aid of
Mark's hyperspace star polytope slicer.
Green's geometry page. Green makes models of regular sponges
(infinite non-convex generalizations of Platonic solids) out of plastic
Hansen-Smith makes geometric art out of paper plates.
- George Hart's
- Chuck Hoberman's Unfolding Structures.
- Houtrust Relief.
Nice photo of a 3d version of one of Escher's bird-fish textures, on the
wall of a water purifying plant in The Netherlands.
The same photographer has several
other Escher photos including one of Metamorphoses in the
Hague post office.
- Hyperbolic crochet coral
reef, the Institute for Figuring.
Daina Taimina's technique for crocheting yarn into hyperbolic surfaces
forms the basis for an exhibit of woolen undersea fauna and flora.
shortbread. The Davis math department eats a Poincaré model
of a tiling of the hyperbolic plane by 0-60-90 triangles.
hyperbolic surface activity page. Tom Holroyd describes hyperbolic
surfaces occurring in nature, and explains how to make a paper model of
a hyperbolic surface based on a tiling by heptagons.
- A hyperboloid
in Kobe, Japan, in the 1940s.
- HyperGami gallery. Paper polyhedral penguins, pinapples, pigs, and more.
- Interlocking puzzle pieces and other geometric toys.
- Aaron Kellner Linear Sculpture.
Art in the form of geometric tangles of metal and wood rods.
Pentominos, Eric Harshbarger. He writes that the hard part was
finding legos in enough different colors.
See also his
- Mathematical balloon
twisting. Vi Hart makes polyhedra and polyhedral tangles from balloons.
lego sculptures and Escher Lego, Andrew Lipson.
correct breakfast. George Hart describes how to cut a single bagel
into two linked Möbius strips. As a bonus, you get more surface
area for your cream cheese than a standard sliced bagel.
in John Robinson's symbolic sculptures. Borromean rings, torus
knots, fiber bundles, and unorientable geometries.
minimal winter's tale. Macalester College's snow sculpture of
Enneper's surface wins second place at Breckenridge.
at the Shopping Mall. Topological sculpture as public seating. From MathTrek.
of Mathematical Machines at the University Museum of Natural Science
and Scientific Instruments of the University of Modena.
Main exhibit is in Italian but there is an English
- Models of Platonic solids
and related symmetric polyhedra.
Klein bottles. From the London Science Museum gallery, by way of Boing
Boing. Topological glassware by Alan Bennett.
- Penrose quilt on a
snow bank, M.&S. Newbold. See also
Clemens' Penrose quilt.
- Pentagonal coffee table with rhombic bronze casting related to the Penrose tiling, by Greg Frederickson.
- Plato, Fuller, and the three little pigs.
Paul Flavin makes tensegrity structures out of ball point pens and
stick bombs, lashings and weavings in the plane, F. Saliola.
Park. An ephemeral outdoor display of geometric art, in Princeton,
New Jersey. From Ivars Peterson's MathTrek.
- Ram's Horn
cardboard model of an interesting 3d spiral shape bounded by a helicoid
and two nested cones.
mathématique sur Bruxelles. Student project to photograph
city features of mathematical interest and model them in Cabri.
- Robinson Friedenthal polyhedral explorations.
- Rubik's Cube
Menger Sponge, Hana Bizek.
- Santa Rosa
Menger Cube made by Tom Falbo and helpers at Santa Rosa Junior College
from 8000 1-inch-cubed oak blocks.
cookies. Actually more like Menger cookies, but whatever.
- The Sierpinski Tetrahedron, everyone's
favorite three dimensional fractal.
Alexander Graham Bell made kites in this shape,
and it has been a frequent construction of geometric model-makers ever since.
3d models made by interleaving two directions of planar slices.
- sneJ made a
Mandelbrot set with sheet plastic and a laser cutter.
- Solid object which generates an anomalous picture.
Kokichi Sugihara makes models of Escher-like illusions from folded paper.
He has plenty more where this one came from, but maybe the others
aren't on the web.
the Petersen Graph Zome Challenge.
David MacMahon discovers that there is no way to make a
non-self-intersecting peterson graph with Zome tool.
Includes VRML illustrations.
- The sphericon,
a convex shape with one curved face and two semicircular edges that can
roll with a wobbling motion in a straight line.
national curve bank sphericon page,
the Wikipedia sphericon page,
Differential Geometry of the Sphericon, and
minaret of Samara.
- Spiral tea
cozy, Kathleen Sharp.
tower. Photo of a building in Iraq, part of a web essay on the
geometry of cyberspace.
- Steve's sprinklers.
An interesting 3d polygon made of copper pipe forms various symmetric 2d shapes
when viewed from different directions.
dodecahedrally decorated Japanese thread ball.
See also Summer's
temari gallery for many more.
- These two pictures by Richard Phillips
are from the now-defunct maths with photographs website.
The chimney is (Phillips thinks) somewhere in North Nottinghamshire, England.
A similar collection of Phillips'
mathematical photos is now available on CD-ROM.
- Three spiral tattoos
from the Discover Magazine Science Tattoo Emporium.
table by Theo Gray, displaying the
of the 3-4-5 right triangle.
- Federation Square.
This building in Melbourne uses the pinwheel
tiling as a design motif. Thanks to Khalad Karim for identifying it.
Photos by Dick Hess, scanned by Ed Pegg Jr.
See this Flickr
photopool for many more photos.
- University of Arizona
mathematical models collection.
- Vasarely Design.
Hana Bizek makes geometric sculptures from Rubik's cubes.
Alberta, home of the world's largest easter egg.
Designed by Ron Resch, based on a technique he
for folding paper or other flat construction
materials into flexible surfaces.
- Voronoi Art.
Scott Sona Snibbe uses a retro-reflective floor to display the Voronoi
diagram of people walking on it, exploring notions of personal space and
Additional Voronoi-based art is included in his
diagrams at the Milwaukee Art Museum. Scott Snibbe's
artwork Boundary Functions,
as blogged by Quomodumque.
zometool design software for OS X and Windows.
(Warning, web site may be down on off-hours.)
- Geometric sculpture by Elias
Water Cube swimming venue at the 2008 Beijing Olympics uses the
Weaire-Phelan foam (a partition of 3d space into equal-volume cells with
the minimum known surface area per unit volume) as the basis of its structure.
- What to make with golf balls? Dale Seymour chooses a Sierpinski triangle and Sierpinski tetrahedron.
thoughts, mathematical knitwear.
Beta. A flexible polyhedron model made by Bathsheba
Grossman out of aluminum, stainless steel, and brass
(bronze optional). Also see the rest of Grossman's
From the Geometry Junkyard,
and recreational geometry pointers.
Send email if you
know of an appropriate page not listed here.
from a common source file.