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