Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:394AG GHM
Order: 20
Horizontal side: 394 Vertical side: 394
Elements: 10√2, 14√2, 20, 19√2, 28, 20√2, 38, 28√2, 40, 56, 40√2, 80, 108, 136, 150, 108√2, 178, 150√2, 244, 197√2.
Code: 2445 0 150 1974 197 197 1783 394 216 196 197 197 387 216 216 106 244 206 207 254 216 206 254 196 407 274 216 406 274 176 807 314 216 1086 286 108 286 216 178 565 244 150 1505 0 0 1504 150 0 140 300 150 1363 286 0 287 286 136 1085 286 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)