From:"Gabor Gevay" <gevay@math.u-szeged.hu>To:"unico" <unico@axelero.hu>Subject:Re: prGRDate:Fri, 19 Sep 2003 23:59:02 +0200

Hi Sa'ndor, These are beautiful - and phantasy-stirring, especially b1. I would coin for it the name "RHOMBIC TRIACOSIOHEDRON", since it has 300 congruent (!) rhombic faces (golden ones I suppose). In addition, it has altogether 600 edges and 280 vertices. Thus its Euler characteristic \chi = F - E + V equals -20. Consequently, its genus g = (1/2)(2-\chi) equals 11. This means that it is topologically equivalent to a doughnut with altogether 11 holes (or, if you like it more, to a sphere endowed with 11 [torus-like] handlebodies). Well, and all this is made of congruent rhombi... (thus it is monohedral). Nice job! I am afraid that facing the exercise: "Find a monohedral (!) non-convex polyhedron with genus 11" would be somewhat frustrating experience to quite a number of people (including geometers). Congratulations! GG ----- Original Message ----- From: unico To: Gabor Gevay Sent: Friday, September 19, 2003 4:23 AM Subject: prGR Helló Gábor, Let me show you some of my models, Sándor