Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:293AA1of2 GHM
Order: 20
Horizontal side: 293 Vertical side: 293
Elements: 16, 16√2, 32, 24√2, 36, 37, 48, 36√2, 48√2, 72, 73, 74, 56√2, 73√2, 74√2, 110, 146, 147, 110√2, 183.
Code: 1837 0 293 1473 183 146 1107 183 293 1106 183 183 375 183 146 366 0 110 727 36 146 160 108 146 161 124 146 485 124 98 484 172 98 1463 220 0 732 293 73 560 92 130 321 124 130 365 0 74 244 148 74 745 0 0 744 74 0 733 293 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)