Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:456AF GHM
Order: 20
Horizontal side: 456 Vertical side: 456
Elements: 16, 16√2, 32, 24√2, 32√2, 34√2, 48√2, 68, 56√2, 63√2, 112, 126, 136, 102√2, 104√2, 131√2, 194, 160√2, 262, 228√2.
Code: 2625 0 194 2284 228 228 1606 296 296 683 296 228 1042 400 192 344 262 194 1026 194 126 1945 0 0 1314 131 63 560 400 192 486 296 88 1127 344 136 1363 456 0 636 131 63 1265 194 0 322 328 56 323 328 24 162 344 40 163 344 24 244 320 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)