~ X.. ov, Jo) Ve Tas UNIVERSITY OF CALIFORNIA, DAVIS BERKELEY 9 DAVIS © IRVINE ® POS ANGELES ® RIVERSIDE © SAN THRGO 2 SAN FRANCISCO SANTA BARBARY © SANTA CRUZ DEPARTMENT OF MATHEMATICS DAVIS. CALIFORNIA 95616-8633 September 6, 1991 Dr. Joshua Lederberg The Rockfeller University 1230 York Ave. New York, NY 10021-6399 Dear Joshua: Sorry it has been so long for my reply to your letters. I have been ill and sometimes even replying to letters seems to be more than I can handle. I was glad to get your second letter pointing out the Hamiltonian circuit in the "Buckyball". I was going to point out that the pictures on the xerox copy you sent me about soccerang show a Hamiltonian circuit in the very same polytope. You asked about other trivalent polyhedra with minimal face ~ size 5. I have enclosed a photocopy of the cyclically 5-connected 3-polytopes with up to 32 vertices (they all have HC’s). Thanks for the article on "Buckyballs", this was new to me and it sounds very exciting. I hope all is well with you. Best regards, David Barnette