Let
be an incidence geometry, i.e., a set with a symmetric, reflexive binary relation
.
Let
and
be elements of .
Let an incidence plane be an incidence geometry whose object set is the disjoint
union of two sets
and
such that for
or ,
only if .
Then a generalized polygon is an incidence plane such that for all ,
1. There exists a path of length at most from to , and.
2. There exists at most one irreducible path of length less than
from
to .
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