What is a Quadrigon?
In EQF (Encyclopedia of Quadri-Figures) a Quadrigon is defined as a system consisting of four random points occurring in a plane and 4 lines connecting these points in a cycle, where a cycle and its reverse cycle are supposed to be the same cycle.
This system is also sometimes called a Tetragon.
The points of a Quadrangle (system of 4 random points) can be cyclically ordered in 3 ways (1-2-3-4, 1-2-4-3, 1-3-2-4).
A Quadrigon can be seen as the representation of one of these permutations.
The lines of a Quadrilateral (system of 4 random lines) can also be cyclically ordered in 3 ways (1-2-3-4, 1-2-4-3, 1-3-2-4).
Again a Quadrigon can be seen as the representation of one of these permutations.
In practice, it also will show that when points of a Quadrangle and points of a Quadrilateral combine, this will happen at the level of a Quadrigon.
A Quadrigon is a flexible framework that can be used to construct many specific objects.
Because the order of points and lines are known terms like "opposite" and "adjacent" play an important role in a Quadrigon.
In EQF these objects often will be prefixed with “QG-”.
< ----- In the column at the left several items and objects can be chosen from Quadrigons.
By clicking at a button at the top of this colomn also objects can be chosen from:
- INDEX QA–1, QA–2 -> Quadrangle-objects-1 and -2
- INDEX QL–1, QL–2 -> Quadrilateral-objects-1 and -2
- INDEX QG–1, QG–2 -> Quadrigon-objects-1 and -2