When a magic square consists out of triangular, square and pentagonal
numbers, it is called a magic square of polygonal numbers. These polygonal
numbers are the amount of dots that fill each next order triangle, square
or pentagon (image left). All 3 triangular, square and pentagonal numbers
start at value 0, followed by 1. Their next values are different. The
triangle consist out of three dots and will respectivly get value 3, the
square 4 and the pentagon 5. From here on out, each shape will grow it's
size by 1, the triangle will contain 6 dots, the square 9 and the pentagon
12. Each of these numbers will be a part of the polygonal magic square. If
all polyonal numbers are used starting from 0 till the $$n^2$$ (n is the order
of the magic square) polygonal number (only taking triangular, square and
pentagons into consideration) that exists, it can be said the polygonal
magic square is
consecutive.
