word  max over all binary tori with <= 20 cells   known C_2 (HS Thm 1.4(c) + Prop 3.1; ABBB: this claim)   shapes attaining the max
AB        3       3   equal   ['1x2', '1x4', '1x6', '1x8', '1x10', '1x12', '1x14', '1x16', '1x18', '2x2', '2x3', '2x4']
ABA       3       3   equal   ['1x2', '1x4', '1x6', '1x8', '1x10', '1x12', '1x14', '1x16', '1x18', '2x2', '2x3', '2x4']
ABB       2       2   equal   ['1x3', '1x6', '1x9', '1x12', '1x15', '1x18', '2x3', '2x6', '2x9', '3x3', '3x4', '3x5']
AABB    3/2     3/2   equal   ['1x4', '1x8', '1x12', '1x16', '2x4', '2x8', '3x4', '1x20', '4x4', '4x5']
ABAB      3       3   equal   ['1x2', '1x4', '1x6', '1x8', '1x10', '1x12', '1x14', '1x16', '1x18', '2x2', '2x3', '2x4']
ABBA      2       2   equal   ['1x3', '1x6', '1x9', '1x12', '1x15', '1x18', '2x3', '2x6', '2x9', '3x3', '3x4', '3x5']
AABA      2       2   equal   ['1x3', '1x6', '1x9', '1x12', '1x15', '1x18', '2x3', '2x6', '2x9', '3x3', '3x4', '3x5']
ABBB    3/2     8/5   below (max needs a larger torus)   ['1x4', '1x8', '1x12', '1x16', '2x4', '2x8', '3x4', '1x20', '4x4', '4x5']
