Last edited 26jan14, previous 7jun99 by gfrancis@uiuc.edu
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Etruscan Venus: Red

(C)1989 Donna Cox, George Francis, Ray Idaszak, NCSA. venus

This surface is a Whitney-stable 3D projection of a nonorientable surface with Euler characteristic 0 (a Kleinbottle) embedded in 4-space. Like Steiner's Roman Surface'', the Etruscan Venus'' loses its singularities under Fran\c cois Ap\' ery's Romboy'' homotopy and becomes an immersed surface equivalent to the connected sum of two copies of Boy's Surface.''

G.Francis, {\sc The Etruscan Venus}. In P. Concus, R. Finn, D. Hoffman (Eds.) {\it Geometric Analysis and Computer Graphics.} Mathematical Sciences Research Institute Publications. Springer-Verlag, N.Y. 1991.

Optiverse: ICM98 Berlin Poster

(C)1998 George Francis, John Sullivan, Stuart Levy optiverse

This image graced the main poster of the International Congress of Mathematicians in Berlin, August 1999. It is a detail of the four "isthmus events" that open/close the ears of Morin's Surface during the eversion of a sphere.

Weaire-Phelan Foam: Relaxed Voronoi Cells

(C) 1999 John Sullivan, Stuart Levy ~jms

The Weaire-Phelan foam is a counterexample to Kelvin's conjecture about the best partition of space into equal-volume cells.

Computer graphic by John M. Sullivan, Math. Dept., Univ. of Illinois.

Optiverse: Minimax Sphere Eversion

(C)1998 John Sullivan, George Francis, Stuart Levy optiverse

The principal stages of this Morin eversion are arranged about the border of this composite.

With the assistance of Camille Goudeseune, the image was raytraced with Renderman on a Silicon Graphics Onyx 2 in the Numerical Laboratory of the National Center for Supercomputing Applications and the VisLab of the Beckman Institute at the University of Illinois at Urbana-Champaign.

This Irisprint was made from its electronic database by Digicolor.

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Dodecaplex

http://new.math.uiuc.edu/~jms/

This image of the dodecaplex graces the August `99 (SIGGRAPH) issue of CACM.