George Hart, a geometric sculptor, scholar and engineer, has been turning math into arts using 3D printer.
In the picture above are acorn-like objects which are solids of constant width in a variety of shapes and made on a 3D printer.
They generalize the Reuleaux triangle to 3D. If you put one between two parallel planes, its width is 1 inch, no matter what direction you measure. If they are resting on a flat table, you can put a sheet of glass on top of them and it slides around while staying perfectly level. A fun toy!
George Hart uses computer technology and solid freeform fabrication designing and fabricating geometric sculpture and is world well-known for its mathematical depth and creative use of materials. He is very active in using 3D printing technology and believe 3D printers will be ubiquitous and inexpensive in 10 years and go into every corner in universities, high schools and shops. The 3D printing technology can turn those 3D and 4D structures into stunning looking objects, even if one doesn't understand the underlying higher-dimensional ideas behind them.
Here are some nice models he has made.
1. The 120 Cell is a 4D structure made of 120 regular dodecahedra. This "shadow" of it has the form of one large dodecahedron filled in with 119 smaller dodecahedra.
The model in the photo is made of stainless steel powder made by the Extrude Hone "ProMetal" process. There are available for purchase at Bathsheba Grossman site.
2. This is a five-inch diameter model of a polyhedron first desbribed by the mathematician Michael Goldberg in a 1937 paper. Hart chose the 972 faces--12 pentagons and 960 hexagons to design and made on a 3D Systems InVision machine.
3. This is a popular fractal, the Menger sponge. Question: What shape is the cross section when one slices a Menger's sponge in half on a plane which is the perpendicular bisector to the cube's long diagonal? You can find answer here.
4. This cool object is made of mylon by SLS with length 5.5 inches. If you like music and geometry you will like it. It is a model of the orbifold representing three-note chord types. Each sphere represents a type of three-note chord, but abstracting away any particular transposition.
5. Below is a a spherical form with 72 open faces and made on a Zcorp machine.
6. Hart owns Makerbot Cupcake and Thing-O-Matic 3D printer that he can create constantly beautiful models. Check out this very nice 12-stick puzzle. There are totally twelve sticks in this puzzle, three in each of four colors. Each has two notches near the middle and a third notch at one end. They are snapped together in a tricky arrangement. If you want to print out and assemble them together, follow the steps here. Isn't it a good idea to make this as a X'mas gift for your family? Can keep them to play with for a while and show off in the school.
7. And another makerbot product: it is a catenary arch made of seven pieces. The puzzle is to assemble them (with no glue) into the arch below. Are you tempted to make your own copy?
(photo credit: George Hart)
George Hart has a nice set of geometrical models models on his site. The great thing about him is that he lets you download his STL files from site and use to build, repost, and modify those stl files in any way you like, as long as you give him credit. You can find the STL file for the above cool objects as well as other stunning stuff at his rapid prototyping page and makerbot constructions page. Many thanks George!
Source: George Hart site
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