Explanation 12x12 magic square

The 12x12 magic square is an odd multiple of 4. To construct a 12x12 magic square there are less methods available than you can use to construct an 8x8, 16x16 or 32x32 magic square. Because 12 is 3x4, it is possible to construct composite magic squares. It is not possible to construct a Franklin (pan)magic 12x12 square, but you can construct an ultra magic or most perfect magic 12x12 square.

Construction methods

The methods to construct a 12x12 magic square are:

• Medjig
• Composite, Simple
• Composite, AxB compact
• Composite, Matroesjka
• Composite, Prop. (1) a
• Composite, Prop. (1) b
• Composite, Prop. (2)
• Symmetric transformation
• Basic key method (ultra magic)
• Most perfect transformation
• Khajuraho method
• Basic pattern method (1)
• Basic key method (most perfect)
• Sudoku method (2)
• 10x10 in 12x12 (1)
• 10x10 in 12x12 (2)
• Concentric
• trimagic

Medjig and composite simple give simple magic squares.

Composite AxB compact, composite Matroesjka, composite proportional (1)a, composite proportional (2), 10x10 in 12x12, concentric and trimagic are 'specials'.

Use symmetric transformation and basic key method (ultra magic) to construct ultra magic 12x12 squares.

With the remaing methods you can construct most perfect magic 12x12 squares.