Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:264AT GHM

Order: 20

Horizontal side: 264 Vertical side: 264

Elements: 12, 12√2, 16√2, 24, 17√2, 24√2, 34, 33√2, 48, 50, 52, 64, 66, 84, 66√2, 82√2, 116, 132, 148, 132√2.

Code: 1487 0 264 843 148 180 507 148 264 336 165 231 667 198 264 666 198 198 170 165 231 347 148 214 820 182 214 643 64 116 127 64 180 126 64 168 247 76 180 246 76 156 487 100 180 525 64 116 164 116 116 1320 132 132 1321 264 132 1167 0 116

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)