7P-s-P1  7P-Schmidt Point

Consider a 7-Point (Heptangle) with vertices Pi (i=1,2,3,4,5,6,7).
Choose one of its vertices Pi.
Construct the perpendicular bisectors Lij of (Pi,Pj), where j unequal i.
In this way, Pi defines a 6-Line (Hexalateral) formed by these perpendicular bisectors.
It appears that the 6L-Schmidt Transformation (6L-s-Tf1) wrt to this 6-Line of Pi is independent of the chosen Pi. This fixed point is 7P-s-P1.
This point was found by Eckart Schmidt. See Ref-34, QFG #3552.

7P s P1 Schmidt Point 01

• In a 7-Point the 7 versions of 6P-s-Ci1 have one common point, which is 7P-s-P1.