Beauty of Magic Squares: 3888-Multiple Order Bordered Magic Squares of Order 132-Part 2

This paper presents a systematic construction of  multiple order bordered magic squares at orders 20, 30, 42, 56, 72, 90, 108 and 132. for a full structural summary. Unlike classical block-wise bordered magic squares, which are built as multiples of a single block size, the structures explored here incorporate successive borders drawn from magic squares of  different orders --- specifically orders 3, 4, 5, 6, 7, 8, 9, 9, 12 --- each contributing a distinct structural layer. The innermost core is a magic square of order~12 formed by different-sum magic squares of order~3.  Successive borders of orders 4, 5, 6, 7,  8, 9, 9 and 12 are then applied; even-order borders consist of equal-sum, while odd-order borders consist of  different-sum magic squares. In case of order 8, first three are of equal-sums and last three are of different sums. The combinatorial multiplicity of border types at each level yields a hierarchy of distinct configurations. The excel file of the work are also attached.

This work is also available at author's web-site.