Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272AR GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 16, 20, 16√2, 32, 40, 29√2, 48, 38√2, 58, 48√2, 76, 78, 80, 58√2, 60√2, 96, 98, 96√2, 107√2, 136√2.

Code: 1362 136 136 1074 107 165 783 214 194 587 214 272 586 214 214 205 214 194 296 107 165 987 136 194 380 234 194 600 196 156 761 272 156 403 136 96 960 96 96 961 192 96 482 240 48 481 240 96 167 240 96 160 256 96 327 240 80 803 272 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)