Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:365AC GHM
Order: 20
Horizontal side: 365 Vertical side: 365
Elements: 36, 26√2, 29√2, 36√2, 58, 72, 58√2, 87, 95, 72√2, 110, 116, 90√2, 131, 95√2, 139, 154, 162, 180, 139√2.
Code: 1627 0 365 900 162 365 1161 278 365 582 336 307 871 365 365 583 336 249 292 365 278 1396 226 139 726 0 203 1807 72 275 260 252 275 1543 226 95 1107 226 249 725 0 131 1395 226 0 1315 0 0 364 36 95 363 72 95 954 131 0 953 226 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)