Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:311AB GHM
Order: 20
Horizontal side: 311 Vertical side: 311
Elements: 20, 21, 28, 20√2, 28√2, 40, 56, 40√2, 56√2, 80, 84, 63√2, 66√2, 105, 112, 84√2, 126, 140, 143, 227.
Code: 2277 0 311 1053 227 206 847 227 311 846 227 227 215 227 206 660 122 206 1261 248 206 632 311 143 1433 311 0 566 0 84 1127 56 140 1403 168 0 207 168 140 200 188 140 407 168 120 400 208 120 565 0 28 807 168 80 285 0 0 284 28 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)