Creepy... 666 <=> Evil Madame Medusa...

Anyway for RW's riddle, I got a non-water tight approach...

Suppose we arrange the unicorns on the perimeter of the field, which has a total length of 24x4=96m, where we can put at most 22 unicorns (in practice only 21, but let's say 22)... Now consider an inner square within the field, of a distance of at least 4.25xsqrt(3)/2~=3.68m from the edges... All points outside this inner square is bound to be closer than 4.25m to the 22 unicorns along the edges of the field, because they're included in one of the equilateral triangles formed by 2 adjacent outside unicorns... So for this inner square, the side is 24-3.68x2=16.64m, with a perimeter of 16.64x4=66.56m, where we can put no more than 15 unicorns. Similarly, forming another "layer" within, the next level is a 9.28m square with perimete=37.12m, allowing 8 more unicorns. At last, we have a 1.92m small square right in the middle, which allow us to put 1 unicorn only. So in total we could at most put 22+15+8+1=46 unicorns...

But I cannot be sure if this approach cover the maximum number of unicorns we could put within the field...