From:           "Gabor Gevay" <gevay@math.u-szeged.hu>
To:             "unico" <unico@axelero.hu>
Subject:        Re: prGR
Date:           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