  We show that Simion's type $B$ associahedron is combinatorially equivalent to
a pulling triangulation of a type $B$ root polytope called the Legendre
polytope. Furthermore, we show that every pulling triangulation of the Legendre
polytope yields a flag complex. Our triangulation refines a decomposition of
the Legendre polytope given by Cho. We extend Cho's cyclic group action to the
triangulation in such a way that it corresponds to rotating centrally symmetric
triangulations of a regular $(2n+2)$-gon. Finally, we present a bijection
between the faces of the Simion's type $B$ associahedron and Delannoy paths.
