Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:256AN GHM
Order: 20
Horizontal side: 256 Vertical side: 256
Elements: 14, 14√2, 28, 21√2, 22√2, 25√2, 28√2, 50, 52, 56, 58, 52√2, 100, 102, 104, 76√2, 77√2, 79√2, 100√2, 102√2.
Code: 1025 0 154 1024 102 154 520 204 256 521 256 256 503 152 154 252 177 179 1041 256 204 790 177 179 772 77 77 764 76 78 226 76 78 587 98 100 1000 156 100 1001 256 100 210 77 77 563 56 0 282 84 28 281 84 56 142 98 42 141 98 56
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)