In the lower diagrams, the four meeting quadrilaterals are moved to the back of the polyhedron (hidden edges shown in green). Since those four quadrilaterals have 8 free edges, the remaining faces can be shown drawn on an octagonal net. Thus each polyhedron is shown twice, once in a square net and again in the octagonal net immediately below it.
In the lower diagrams, the three quadrilaterals are moved to the back of the polyhedron (hidden edges shown in green). Since those three quadrilaterals have 8 free edges, the remaining faces can be shown drawn on an octagonal net. Thus each polyhedron is shown twice, once in a square net and again in the octagonal net immediately below it.
We also cannot have four quadrilaterals forming a strip because that configuration requires ten vertices.
We also cannot have a cluster of 3 quadrilaterals and another of two not joined edge to edge. A cluster of three quadrilaterals requires eight vertices and that would leave only one vertex for the remaining pair of quadrilaterals.
