Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:311AA GHM
Order: 20
Horizontal side: 311 Vertical side: 311
Elements: 3, 20, 28, 20√2, 28√2, 40, 56, 40√2, 42√2, 56√2, 80, 84, 63√2, 112, 84√2, 126, 129, 140, 143, 227.
Code: 2277 0 311 560 227 311 561 283 311 282 311 283 281 311 311 1403 311 143 1293 171 126 1127 171 255 207 171 143 206 171 123 407 191 143 406 191 103 807 231 143 1433 311 0 420 42 126 1261 168 126 632 231 63 31 171 126 847 0 84 840 84 84
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)