Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:388AD GHM
Order: 20
Horizontal side: 388 Vertical side: 388
Elements: 8√2, 14, 16, 12√2, 16√2, 24, 20√2, 23√2, 32√2, 46, 37√2, 74, 60√2, 120, 148, 120√2, 134√2, 148√2, 240, 194√2.
Code: 2405 0 148 1944 194 194 1346 254 254 376 217 217 745 254 180 230 217 217 461 240 194 145 240 180 162 256 164 241 264 180 122 276 168 324 296 148 600 328 180 200 276 168 163 256 148 82 264 156 1485 0 0 1484 148 0 1200 268 120 1201 388 120
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)