Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272AO GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 3√2, 6, 21√2, 26√2, 42, 51, 52, 45√2, 47√2, 48√2, 52√2, 84, 94, 96, 105, 78√2, 84√2, 89√2, 94√2, 110√2.

Code: 1102 110 162 894 89 183 476 131 225 947 178 272 946 178 178 423 131 183 965 131 129 214 110 162 1053 131 78 515 131 78 484 179 81 450 227 129 36 179 81 67 182 84 840 188 84 841 272 84 260 26 78 784 104 0 527 0 52 520 52 52

The properties below may precede order:side in a tiling's title:

• c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
• d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
• e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
• i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
• r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.

Credit for Discovery

Just three people are credited with the discovery of Primitive Perfects:

Geoffrey H. Morley (GHM, England)

Jasper D. Skinner, II (JDS, United States)

William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)