Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:382AF GHM
Order: 20
Horizontal side: 382 Vertical side: 382
Elements: 3√2, 8√2, 48√2, 52√2, 74, 56√2, 80, 96, 104, 74√2, 111, 112, 117, 148, 108√2, 154, 111√2, 160, 117√2, 154√2.
Code: 1607 0 382 1080 160 382 1114 271 271 1113 382 271 526 0 222 1047 52 274 566 100 218 1127 156 274 30 268 274 1170 265 271 1171 382 271 1485 0 74 480 100 218 961 148 170 82 156 162 807 148 154 1540 228 154 1541 382 154 745 0 0 744 74 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)