Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:382AB GHM

Order: 20

Horizontal side: 382 Vertical side: 382

Elements: 21√2, 30√2, 46, 46√2, 52√2, 74, 78, 88, 92, 104, 78√2, 134, 96√2, 138, 104√2, 148, 156, 117√2, 122√2, 152√2.

Code: 1522 152 230 1224 122 260 923 244 290 1387 244 382 1176 265 265 306 122 260 1345 152 156 464 198 244 463 244 244 210 265 265 881 286 244 962 382 148 743 152 156 786 0 78 1565 78 0 1044 182 52 1043 286 52 1483 382 0 785 0 0 524 234 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)