Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:253AA GHM

Order: 20

Horizontal side: 253 Vertical side: 253

Elements: 13, 13√2, 17√2, 26, 22√2, 39, 44, 55, 39√2, 76, 55√2, 78, 88, 89, 100, 76√2, 110, 82√2, 88√2, 99√2.

Code: 992 99 154 824 82 171 263 164 227 132 177 240 891 253 253 133 177 227 762 253 164 390 138 227 391 177 227 176 82 171 787 99 188 1003 177 88 763 253 88 443 99 110 556 0 55 1105 55 0 224 77 88 884 165 0 883 253 0 555 0 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)