On this page will be pictures of sculptures I made in Fall 2012 and Spring 2013. In Fall 2012 I made one bronze sculpture shown below, a torus 6" in diameter with three linked circles on it surface, dividing the surface into three separate valleys. This is the cast bronze version of the carved wood torus links sculpture shown on the page with sculptures from Spring and Summer 2012, where you can also see the wax model used to make this piece. This sculpture was cast at the bronze pour held in November 2012 at the Binghamton University Sculpture Studio.
The next pictures show a carved (5,3) torus knot made from Claro Walnut, 8" in diameter, started during the summer 2012 and finished on 1-3-2013. This knot is the dual to the (3,5) torus knots previously made, since the knot in this sculpture goes around the torus 5 times and through the center hole 3 times before returning to its beginning.
The next pictures show a (4,5) torus knot carved from Zebrawood, 6" in diameter, 3" thick, completed on 1-12-2013.
In Fall 2008 I completed a large bronze sculpture of a figure eight knot whose cross section was a hypocycloid, similar to the smaller one I made in Spring 2008. In both of these the design includes a Mobius twist along the length so that there is a single edge running three times around the knot before returning to its beginning, and similarly for the single surface. Since then I have wanted to try to use this design to make a jewelry-size piece in silver. On Jan. 23, 2013, the excellent jeweler-artist, Bill Clune of Ithaca, NY, created a prototype of this design in Sterling silver from a piece of triangular silver wire using my design. The width of the piece is approximately 1.25". We are exploring cost effective methods of reproducing this design, which also incorporates features of a Mobius strip, since it has only one edge and one side.
On Jan. 27, 2013 I completed a 6" diameter carved torus link sculpture from Bubinga wood. It can be thought of as having two distinct (2,1) knots on its surface, each of which goes around the outside of the torus two times and through the hole once before coming back to its beginning. That divides the surface into two unconnected valleys, each of which does the same as each of the knots, going around twice and through the hole once. If this were made of a flexible rod material, with cross section a square (with concave sides), it would be created by bending the rod into a circle with a 180 degree twist so that opposite sides of the square would meet when the circle closes. The pictures show both sides, a view from the side, and a closeup showing details of the wood grain.
On February 25, 2013, I completed two more small ``twist" sculptures, carved from the center cylinder removed to make the hole in a larger carved torus knot sculpture. They are each 2" tall, 1.5" in diameter, one of cocobolo, the other of jobillo.
On April 5, 2013, a bronze casting was made at the Sculpture Studio at Binghamton University of a figure eight knot with circular cross section. The model was made from polyethylene rod rather than wax, with a steel wire embedded along the length to allow it to keep its shape. The gating was also made from polyethylene, with just some wax at the joints to smooth connections. The first picture below shows the result after all the gating had been cut off, but before other polishing had begun. The next two pictures show the piece after more polishing, but before any welding repairs were done. This piece is approximately 17" x 15" x 13" in size, and will be mounted on a stone base hanging from a bronze arch. Even at this stage this sound sculpture has a nice tone when struck. The last two pictures show the piece after all welding repairs have been done, and some polishing, mounted over a bluestone base hanging from an arch.
On April 26, 2013, the eighth annual iron pour was held at the Sculpture Studio at Binghamton University, with students from 10 colleges and universities participating. I cast one piece, a (4,5) torus knot intended to be a better version of the one I made in 2011. Due to difficulties making the inner core and positioning it firmly, it appears that the inner core moved (floated) during the casting process, leading to one side being too thick and the other side being too thin, and not all of its surface was done. I am in the process of trying to repair this with welding. The first two pictures below show the underside and the overside, with gating still attached and no repairs or polishing done. The second two pictures show the piece after some repairs and welding have been done to fill the holes and reshape the bad side. It is shown mounted on a bluestone base with a spherical mirror underneath.
On July 28, 2013, I completed three more small ``twist" sculptures, each carved from the center cylinder removed to make the hole in a larger carved torus knot sculpture. They are 2.75", 2.5", 1.75" tall, and 2.25", 1.5", 1" in diameter, and made from Timborana, Coolibah Burl Red, Tasmanian Eucalyptus Burl, respectively. When the larger torus knot sculptures are completed, their pictures will be posted here.
The following two pictures show the two sides of a (3,5) torus knot I completed July 30, 2013, made from a 2"x4"x4" block of Tasmanian Eucalyptus Burl. The final size of the piece was 3.75" in diameter, 1.75" thick.
The following three pictures show a (4,5) torus knot I completed August 8, 2013, made from a 2.75"x6"x6" block of Coolibah Burl Red. The final size of the piece was 5.75" in diameter, 2.5" thick.
To see more types of sculpture I have tried, follow the following links:
Links back to:
Webpage of Alex Feingold,
Department of Mathematical Sciences,