Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:292AS1of2 GHM

Order: 20

Horizontal side: 292 Vertical side: 292

Elements: 1√2, 2, 2√2, 4, 3√2, 7, 7√2, 13, 34, 34√2, 68, 88, 68√2, 102, 122, 88√2, 136, 102√2, 170, 190.

Code: 1907 0 292 1223 190 170 1027 190 292 1026 190 190 135 190 177 77 190 177 70 197 177 34 200 174 10 203 177 20 202 176 21 204 176 882 292 88 41 204 174 686 0 102 1367 68 170 1703 204 0 685 0 34 883 292 0 345 0 0 344 34 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)