6L-s-P1: 6L-Conical Center

In a 6-Line we have 6 Component 5-Lines.
When constructing 6 times the Inscribed Conic Centers (5L-s-P1) of the Component 5-Lines they are coconic. The center of the conic of these centers is 6L-s-P1.
This feature cannot be extrapolated to a 7-Line.
6L s P1 Conical Center 00

See also the note at 6L-s-Co1.