Perimeter Magic Polygon >k=3

These are the six possible solutions for order 3. They are in sorted order with 1 and 6, 2 and 5, 3 and 4 the complement pairs.
Order 4 has a total of 146 basic solutions (I think). Here are four.
Some examples for higher orders of perimeter magic squares.
[1] Terrel
Trotter, Jr., Normal Magic Triangles of Order n, Journal of Recreational
Mathematics, Vol. 5,, No. 1, 1972, pp.2832 These are the only order3 perimeter magic pentagons (not
counting the 4 rotations and 5 reflections of each). These six solutions are shown arranged in complement pairs.
This table shows relevant information for 5 sided PMPs.
The following four perimeter magic pentagrams were constructed with the help of a simple routine (once the smallest odd and even orders are designed. Divide the extra numbers required into pairs with equal sums. Then add one of these pairs to each side of the original PMP to get the next larger order of the same parity. In this case, to obtain the order 6 PM pentagon, partition the extra numbers (16 to 25) into 5 pairs each totalling 41. Then add one of these pairs of numbers to any side of the originating order 4.
The 20 basic solutions for order 3 Hexagons # A B C D E F S Comp. # 1 1 11 5 10 2 12 3 8 6 4 7 9 17 19 2 1 11 5 9 3 12 2 8 7 4 6 10 17 20 3 1 11 5 8 4 10 3 12 2 6 9 7 17 18 4 1 12 6 2 11 5 3 9 7 4 8 10 19 14 5 1 11 7 9 3 4 12 2 5 6 8 10 19 7 6 1 9 8 6 4 12 2 11 5 3 10 7 18 17 7 1 11 8 7 5 3 12 2 6 4 10 9 20 5 8 1 10 8 4 7 9 3 11 5 2 12 6 19 10 9 1 10 8 2 9 6 4 12 3 5 11 7 19 15 10 1 11 8 2 10 4 6 9 5 3 12 7 20 8 11 2 12 6 4 10 1 9 3 8 5 7 11 20 16 12 2 12 6 3 11 5 4 7 9 1 10 8 20 13 13 2 10 7 1 11 5 3 12 4 6 9 8 19 12 14 2 11 7 1 12 3 5 9 6 4 10 8 20 4 15 2 8 10 1 9 7 4 11 5 3 12 6 20 9 16 3 12 4 10 5 8 6 2 11 1 7 9 19 11 17 3 10 8 2 11 1 9 7 5 4 12 6 21 6 18 4 7 11 1 10 3 9 5 8 2 12 6 22 3 19 6 9 7 5 10 1 11 3 8 2 12 4 22 1 20 6 9 7 3 12 2 8 4 10 1 11 5 22 2 Three examples
Three order 4 perimeter magic hexagons with consecutive vertex numbers. All solutions for order4 PM Hexagons have not yet been compiled (to my knowledge), so we cannot assign solution numbers to these figures.
