Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:340BC GHM

Order: 20

Horizontal side: 340 Vertical side: 340

Elements: 12, 12√2, 24, 18√2, 36, 32√2, 36√2, 37√2, 64, 74, 84, 64√2, 74√2, 106, 128, 138, 101√2, 106√2, 202, 234.

Code: 2345 0 106 2021 202 340 1012 303 239 1381 340 340 370 303 239 643 266 138 742 340 128 741 340 202 324 234 106 843 266 54 1283 340 0 1067 0 106 1060 106 106 644 170 42 120 182 54 121 194 54 365 194 18 364 230 18 241 194 42 184 212 0

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)