Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:462AC GHM
Order: 20
Horizontal side: 462 Vertical side: 462
Elements: 17√2, 20√2, 34, 40, 34√2, 40√2, 60, 51√2, 80, 72√2, 110, 80√2, 140, 110√2, 182, 140√2, 200, 220, 242, 322.
Code: 3227 0 462 2423 322 220 1407 322 462 1406 322 322 512 373 271 170 373 271 340 356 254 341 390 254 722 462 182 806 0 140 2007 80 220 2203 280 0 1102 390 110 1101 390 220 1823 462 0 805 0 60 605 0 0 404 40 20 403 80 20 204 60 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)