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An "irregular" polyhedron, by abuse of notation, is a polyhedron for which three faces meet at each vertex, and no two adjacent faces have the same number of sides. Apparently, only five different such polyhedra have no faces with more than 7 sides. This one consists of four heptagons, four hexagons, four pentagons and six quadrilaterals.
At one point, I thought there were only four of these polyhedra. This one, which has the same number of faces of each type as no. 3, was discovered while I was trying out a home-made algorithm for traversing planar triangulations (as opposed to plantri, which I did not manage to install).