Originally Posted by **ticbol**

So Steiner points they are.

About that symmetry of the network again. Again, follow Steiner. Drop a line along that axis of symmetry. Stop a some random point 7. Draw two rays that are 120 degrees to the right or to the left of that starting line/axis.

On one of the two rays, proceed, then stop at some random point 6. Align this point six, and also the point 7, so that the next two rays fromt point 6 will hit points 4 and 5. There you have the left half of the network.

Now go to the right half. Do the same thing---stopping at some point 8, drawing two rays from point 8, adjust, adjust until these last two rays hit corners 2 and 3.

Is there a possibility that the right half of the network not a mirror image of the left half, relative to the said axis of symmetry of the regular pentagon?

None.