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## Cycle sequences of crystal structures
For purposes of zeolite topology a T with
the property that the _{i}T's _{i}(i = 1, 2,
...., k) are all different and that each
T is connected to _{i}T
via an oxygen bridge (for other structures an atom binding may be
more appropriate to be used). The number _{i+1}k is called the
length of the cycle. The cycle sequence C(T) of
the atom T is then defined as the sequence
c in
which each term _{3}, c_{4},..., c_{n},...c is equal to the number of
cycles of length _{n}n to which the atom T belongs.
Note that cycles of lengths 1 and 2 are undefined, as they
do not appear for crystal structures.The cycle sequences of the tetrahedral atoms of more than 100 zeolites are accessible via the accompanying table. The sequences were calculated with the program TOPOLAN. Cycle sequences are not restricted to zeolites and the above
definition can be easily generalized in order to be applicable to
all kinds of crystal structures. For example, the cycle sequence
of a vertex of the 2-dimensional square net is the sequence Cycle sequences have been developed by Prof. W.E. Klee and Georg Thimm, both welcoming questions and comments. Page maintained by Georg Thimm
[This is a copy of the page http://www.drc.ntu.edu.sg/users/mgeorg/zeolites/cycles.html made on August 28, 2000 in order to avoid problems with broken links.] |

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