nG-1  Systematics for describing n-Gons

There are specific Points/Line/Curves related to n-Gons because n-Gons create a configuration where the order of reference points/reference lines are important and the property of order is used in the construction of these Points/Lines/Curves.
n-Gons are figures made up from n Points cyclically connected by n Line segments (representing n Lines). It is a bounded figure. Contrary to n-Points and n-Lines order does matter.
Dealing with an n-Point/n-Line (where order does not matter) we can imagine that a distinct number of sets of ordered Points/Lines can be formed from the unordered points/lines.
Therefore any n-Point or n-Line contains a certain number n-Gons, just like an n-Point or n-Line contains a certain number of triangles.
In fact the number of n-Gons in an n-Point or n-Line is the number of combinations of numbers 1, …, n being ordered cyclically, where opposite orders are supposed to equalize the normal order.
Here combinatorics enters the geometry of poly-figures.
The number of n-Gons being contained in an n-Point or n-Line is (n-1)!/2.
For example in a Quadrangle (a 4-Point) we have (4-1)!/2 = 3 Quadrigons (= 4-Gons).
In a Pentangle (a 5-Point) we have (5-1)!/2 = 12 Pentagons (= 5-Gons), etc.
In a Hexangle (a 6-Point) we have (6-1)!/2 = 60 Hexagons (= 5-Gons), etc.
Just to show the difference in n-gons here some regular forms are shown occurring in a regular n-Point, although normally their forms won’t be regular. In an n-Line other figures will occur.
The number of 4-Gons (bounded figures) in a 4-Point is 3:

 nG n 1 n Gons in a 4 Point

The number of 5-Gons (bounded figures) in a 5-Point is 12:

 nG n 1 n Gons in a 5 Point

The number of 6-Gons (bounded figures) in a 6-Point is 60:

nG n 1 n Gons in a 6 Point