Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:388AE GHM
Order: 20
Horizontal side: 388 Vertical side: 388
Elements: 8, 10√2, 20, 20√2, 25√2, 30√2, 50, 52, 40√2, 46√2, 48√2, 52√2, 96, 96√2, 98√2, 146, 121√2, 146√2, 242, 194√2.
Code: 2425 0 146 1944 194 194 986 290 290 963 290 194 522 342 238 523 342 186 462 388 192 484 242 146 83 290 186 966 292 96 400 282 186 304 312 156 206 322 166 106 312 156 205 322 146 1465 0 0 1464 146 0 256 267 121 507 292 146 1210 267 121
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)