Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:254AC GHM

Order: 20

Horizontal side: 254 Vertical side: 254

Elements: 5√2, 28, 28√2, 48, 36√2, 52, 56, 42√2, 62, 52√2, 76, 84, 62√2, 88, 98, 104, 78√2, 114, 83√2, 88√2.

Code: 987 0 254 563 98 198 282 126 226 1041 202 254 522 254 202 521 254 254 283 126 198 765 126 150 1143 254 88 426 0 156 847 42 198 483 126 150 782 78 78 366 42 114 625 78 88 624 140 88 52 83 83 884 166 0 883 254 0 830 83 83

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)