More than Three Polygons

In a previous problem,
Three Polygons, I asked:
Three regular polygons, all with unit sides, share a common vertex.
Each polygon has a different number of sides,
and each polygon shares a side with the other two; there are
no gaps or overlaps. Find the number of sides for each polygon.

I now expand on that idea:
If the restriction that each polygon has a different number of sides is
removed, how many more solutions are there? There can be more than three
polygons (up to six triangles). What are all the possible combinations?

In a plane, one set of polygons may be found at one vertex,
while different sets could be found at others. There could be all
triangles (1 unique polygon), or a combination of triangles and hexagons
(2 unique polygons), and others.
What is the largest number of unique polygons which can tile a plane?
Source: Original.
Solution
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