Considering a
(2n + 2)
-polygon
P
, a geometric realization was proposed for cluster algebra
\mathcalB
of type
B. As an application, a cluster expansion formula was presented for each cluster variable of
\mathcalB and the relationship between clusters of
\mathcalB and triangulations of
P were clarified. At the same time, the correspondence between orbit flips of
\sigma 
-invariant triangulations
\varGamma 
and mutations of clusters of
\mathcalB was constructed based on a designed commutative diagram.
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