  The Interval poset of a permutation is an effective way of capturing all the
intervals of the permutation and the inclusions between them and was introduced
recently by Tenner. Thi paper explores the geometric interpretation of interval
posets of permutations. We present a bijection between tree interval posets and
convex polygons with non-crossing diagonals, offering a novel geometric
perspective on this purely combinatorial concept. Additionally, we provide an
enumeration of interval posets using this bijection and demonstrate its
application to block-wise simple permutations.
