Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:234AJ GHM

Order: 20

Horizontal side: 234 Vertical side: 234

Elements: 6, 6√2, 15, 29, 36, 29√2, 30√2, 44, 48, 36√2, 54, 58, 44√2, 48√2, 73, 88, 102, 117, 132, 117√2.

Code: 1325 0 102 1174 117 117 1173 234 117 151 132 117 297 132 117 290 161 117 731 234 117 1025 0 0 484 48 54 483 96 54 367 96 102 366 96 66 587 132 88 883 190 0 442 234 44 62 102 60 63 102 54 302 132 30 541 102 54 443 234 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)