Square Symmetries
Harmony Worldwide · 2×2 Positional Invariance · Christopher Seekins
Square Symmetries · 19 of 40 elements participate in 2×2 square symmetry. Three groups (a, b, c) each contain four columns arranged as two 2×2 pairs. Groups a, b, and c show identical elemental category positions which are highlighted in yellow. The charge balance for each square are as follows: a's: +, −, +, N  |  b's: +, N, N, N  |  c's: −, −, −, +
Square a · cols 6, 9, 12, 3 1a: col 6 · +  |  2a: col 9 · −
3a: col 12 · +  |  4a: col 3 · N
19 of the 40 elements in each square, share category position
Square b · cols 7, 10, 1, 4 1b: col 7 · +  |  2b: col 10 · N
3b: col 1 · N  |  4b: col 4 · N
19 of the 40 elements in each square, share category position
Square c · cols 8, 11, 2, 5 1c: col 8 · −  |  2c: col 11 · −
3c: col 2 · −  |  4c: col 5 · +
19 of the 40 elements in each square, share category position
+,+,−,−,N,−,+,N,−,N,N,+ — the 12-column charge sequence derived from atomic mass ÷ 3.
The Maltese Cross below connects the square positions (1a, 2a, 3a) to nodes on the 12-spoke wheel.
Square Symmetries — Maltese Cross
Maltese Cross · 1a, 2a, 3a node positions · Harmony Worldwide · Christopher Seekins