Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:264AG7of8 GHM
Order: 20
Horizontal side: 264 Vertical side: 264
Elements: 8√2, 16, 16√2, 19√2, 28, 32, 24√2, 38, 28√2, 33√2, 48, 38√2, 56, 66, 66√2, 104, 132, 99√2, 113√2, 132√2.
Code: 1325 0 132 1324 132 132 1136 151 151 190 151 151 662 66 66 661 66 132 332 99 99 1041 170 132 485 170 84 990 99 99 565 170 28 244 194 60 80 218 84 160 210 76 161 226 76 382 264 38 321 226 60 383 264 0 284 198 0 283 226 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)