5 fold symmetry

Kevin M Jude kjude at mail1.sas.upenn.edu
Fri Nov 19 12:56:41 EST 2004

jodhbir (jodhbir at gmail.com) wrote:
: Hi,
: For non crystallographic structures 5 fold symmetry is allowed but it
: is not allowed for crystallographic structures. Can someone please
: shed some light on this?

For the same reason that soccer balls have black hexagons. 
Crystallographic symmetry must propagate through a plane, while NCS is not
propagated.  If you want to tile a floor with regular n-gons, the angle of
the n-gon must be a whole divisor of 360 degrees.  For n=3, angle = 60 =
360/6; for n=4, angle = 90 = 360/4; for n=5, angle = 108 = 360/(10/3). 

(leaving n=2 , 360/oo as an exercise for the reader...)

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