Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:296AC1of2 GHM

Order: 20

Horizontal side: 296 Vertical side: 296

Elements: 8, 8√2, 16, 16√2, 28, 32, 28√2, 32√2, 37√2, 46√2, 51√2, 74, 56√2, 102, 74√2, 120, 97√2, 148, 111√2, 148√2.

Code: 1482 148 148 1114 111 185 740 222 296 741 296 296 376 111 185 1487 148 222 1203 296 102 516 97 97 286 148 74 87 176 102 80 184 102 564 240 46 1023 296 0 970 97 97 167 176 94 160 192 94 327 176 78 320 208 78 285 148 46 464 194 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)