degenerate polyhedra as double polygons

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Suppose with the term polyhedra we mean every collection of polygons that any two members can alwaysbe jointed together with a polygonal line passing from the interior of some of the edges of others.

I would like in this collection also to include doubly covered polygons i.e polygons with two faces. enter image description here

In order to do that I am thinking of ''allowing'' in the collection to include double elements, like {a,a,b,c} meaning in that case , that double 'a' is considered as double polygon (so $\{a,a,b,c\}\neq \{a,b,c\}$).

Is that definition ok, from the logic point of view?

If not how can I resolve this problem?

Thanks.

Last Edit

I am thinking of defining a collection of polygons $T$, like:

$T=\{(a,2),(b,1),(c,1)\}$, where $1$ means that there is only one such polygon in $T$ and $2$ means that there are $2$ copies of such polygon, i.e doubly covered, in the collection $T$.