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These are two-coloured cards with n=4k+1 edges and the following set of degrees: -- all black vertices are of degree 4, except one, which is of degree 1; -- all white vertices are of degree 2, except one, which is of degree 1; -- and all faces are of degree 4, except one, which is of degree 1.
This already raises the question of enumeration. For example, there are two cards for n=5; only one for n=9; there are no such cards for n=21; there are three for n=25; four for n=65; no such cards for n=69; and so on. The answer to the enumerative question is much more interesting than you might think.
These cards also have other remarkable properties. For example, they can be composed, and this operation is commutative.

Salle 76