Benno Artmann

Mathematical sculptures

Benno Artmann was born in 1933. In post-war Germany, he worked for a few years as a bricklayer, started school again and got his PhD in mathematics in 1965. He was a professor at the mathematics department at the Technical University in Darmstadt and, after his retirement in 1998, came to Goettingen, where he started part-time teaching at the Mathematisches Institut. His hobby is sculpturing. In the early 80s he was inspired by papers of George Francis (whom he knows from their common time in Ann Arbor) and Thomas Banchoff in the Math Intelligencer to do mathematical sculptures. Everything is done by hand.

1. Klein Bottle (1987) marble, 13 cm across.

2. Fish (1993) plaster, length 70 cm. Sphere with two cross caps, another version of the Klein Bottle.

3. Torus with cross cap (2002) wood, 31 cm across. Topologically equivalent to a sphere with three cross caps.

4. Boy`s Surface with 4 windows (1982) plaster, height 40 cm. After an idea of George Francis.

5. S(1) x S(2) (1990) plaster, height 95 cm. (The „foot“ is topologically trivial)

6. 3-Sphere decomposed into two tori with Hopf-fibers indicated (1988) plaster, height 35 cm.

7. 3-Sphere Heegaard-decomposed into two pretzels (1989) plaster, height 61 cm.

8. Lawson`s minimal surface (1986) marble, height 30 cm. After a picture by U. Pinkall.

9. Projection of the 16-cell in R(4) into R(3). (2004/5) glass, 37 cm across. The vertices are the Elements of the quaternion group.

10. 4-cube with the base-quadrangels of the octahedra of the 24-cell indicated. The 24 octahedra of the 24-cell come in 4 tori of 6 octahedra each, first such pictures by Thomas Banchoff.

11. Projection of (part of) the 24-cell into R(3). (2004/5). The red vertices indicate the 8 Elements of the quaternion group.

12. The four tori (of 6 octahedra each) of the 24-cell cut up. (2004/5) Paper, height 50 cm. (B.A. with students.)