hmm ok i guess you COULD be beyond one end of it in a funny stretched ovaly polygon - and then you couldn't be perpendicular to it at all...

i've forgotten the rule now...
it can't work on irregular ones can it?
or was that the point?....

not woken up yet...

It does work on irregular polygons, provided all their sides are the same length and they're convex. For example, it does work for the house-shaped pentagon I described above: for any point within the house shape, the sum of the perpendicular distances from all five sides is a constant.

... *thinks* i was thinking of the dist between the point and the base... not the sides
oops.
still not 100% convinced... need to get a piece of paper!
is it the sum of ALL the sides then?
that would help :)