Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:394AH1of2 GHM
Order: 20
Horizontal side: 394 Vertical side: 394
Elements: 4, 4√2, 8, 8√2, 20, 24, 18√2, 28, 20√2, 46, 64, 55√2, 64√2, 110, 110√2, 156, 174, 165√2, 174√2, 284.
Code: 2847 0 394 640 284 394 641 348 394 202 368 374 461 394 394 203 368 354 82 376 366 83 376 358 182 394 348 45 368 354 44 372 354 283 376 330 247 348 354 1746 220 174 1656 55 165 1567 220 330 1745 220 0 550 55 165 1107 0 110 1100 110 110
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)