Now it should go on here. Namely, it is possible to generate further variants of labyrinths by simply rotating the polygon used.
I take again the net with the polygon from the last post on this topic (part 2).
This diagram can be used to create four different labyrinths. Two directly (line 2 and 3), the other two by a simple calculation.
Other constellations can be gained by rotating the network 12 times by 30 degrees. Or in other words, it’s just like changing the clock for the summer or winter time.
Since only interesting labyrinths are of interest here, I omit all positions where the lines would point to the first and / or last circuit. So from the 12 you should not reach the 1 or the 11. Only the “times” are interesting, which point farther away, that is, run more sharply.
That would be in the above net the 1, 5 and 6. So I turn only to these times. In other words, I bring the 1, 5, and 6 into alignment with the 12. I turn the net by 30, 150, and 180 degrees. To rotate is the net with the polygon, the numbers stay in place.
Here’s the first turn:
I get four completely different path sequences than in the original above.
The second rotation:
I get four new variants again.
The last rotation:
Here I just get a different order of the sequences than in the original polygon. So there are no new variants, just another arrangement. This is because the rotation of 180 degrees corresponds to a symmetrical reflection.
It is not always possible to find new variants. With the help of this net I have generated a total of 12 different path sequences for 12 new labyrinths.
The path sequences can be directly converted into a labyrinth drawing.
Here only one (again in concentric style) is to be shown (the 2nd path sequence from the first polygon above):