Symlateral Magic Squares

Description

These squares have complementary numbers that:

See symlateral.

These can be transformed from/to concentric magic squares by repeating transform 2. Swap all pairs of rows on the top side of the square in increasing sequence, e.g., for orders 9 and 10, swap rows (1 2), (1 3), (1 4), (2 3), (2 4), (3 4).

Construction

SymlateralSquares makes these squares.

Odd Order Squares

Example Squares: Order 5, 7

Order 5, 7 squares

The center 3x3 square can be any center of an odd concentric magic square of the same order including any aspect of the Lo Shu square.

Bones of Above Squares

Order 3, 5, 7 bones

Each order n bones is conceptually made from the n-2 bones by:

Even Order Squares

Example Squares: Order 6, 8

Order 6, 8 squares

The center 4x4 square can be any center of an even concentric magic square of the same order including any aspect of the 880 order 4 squares.

Bones of Above Squares

Order 4, 6, 8 bones

These are conceptually made as for odd order bones, but reserving two middle rows and columns here, (see octant boundaries).

Note 1: ½ has been omitted from all the bones numbers displayed here. Therefore, to convert these displayed bones numbers to the actual square numbers:

Note 2: Here the outside cells of the middle rows and middle columns are not middle symmetric.