What is an n-Point?

In EPG (Encyclopedia of Poly Geometry) an n-Point is defined as a system consisting of  'n' random points occurring in a plane, no three of which are collinear.
There are no lines involved. There is no order in these points. Just 'n' random points. Nothing more and nothing less.
Every point in an n-Point is exchangeable with one of the other points.
Whatever is valid for a subset of these points is also valid for another subset of equal amount of these points.
An n-Point is a flexible framework that can be used to construct many objects upon.
In EPG these objects often will be prefixed with “nP-”.

Just like in a triangle and in a quadrangle new (derived) points can be developed.
These new points will be called ‘points’ or ‘centers’.
They will be noted with codes nP-n-Px or nP-s-Px (x=serial number).
The prefix “nP” means that we deal with an n-Point.
“n” can be substituted by a natural number.
When the infix is “n” then the point occurs for all natural n.
When the infix is “s” then the point occurs for only one specific n.
The suffix “Px” tells that we deal with a Point with serial number x.
Apart from Points also Lines, Circles, Conics, Cubics, other Curves, Transformations, Triangles can be constructed, then the suffixes resp. will be Lx, Cix, Cox, Cux, Cvx, Tfx, Trx, where x is the serial number for this category.

Examples:
nP-n-P1 = the point P1 existing in a 3-Point, 4-Point, 5-Point, 6-Point, etc.
5P-n-P1 = the point nP-n-P1 as occurring in a 5-Point.
5P-s-P1 = the point P1 which is only and specifically occurring in a 5-Point.
So there are different series of points in the nP-n-range, 3P-s-range, 4P-s-range, 5P-s-range, etc.
Points (Centers) in the nP-n-range are centers constructed in a recursive way to a higher level. Each higher level is one more reference point in the n-Point.

Related to an n-Point several point, lines, circles, conics, cubics, transformations and triangles do exist, which can be obtained from the pulldown menu at the left of this page.
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