Let h6 denote the standard regular hexagon, inscribed in the unit circle and its first three vertices B(1,0), C(cos(pi/3),sin(pi/3)) and D(cos(2*pi/3),sin(2*pi/3)).
Every symmetric hexagon is homographic with an hexagon defined by the two vertices B, C, an additional point A and their symmetrics to the origin. When A coincides with D the hexagon is the regular unit hexagon (h6). Point A is free movable. Each one of the various exagons (h), for various places of point A, is a representative of a whole class of homographic hexagons. The other symmetric hexagons of the class are obtained by applying to (h) an homography whose matrix is of the type:
| a b c |
| d e f |
| 0 0 1 |
![[alogo]](alogo.png){kind=small}
Symmetric hexagons ![[0_0]](Symmetric_hexagons_All_files/Symmetric_hexagons_All_0_0_0.png)
![[1_0]](Symmetric_hexagons_All_files/Symmetric_hexagons_All_0_1_0.png)