Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:394AJ2of2 GHM
Order: 20
Horizontal side: 394 Vertical side: 394
Elements: 4, 4√2, 8, 6√2, 12, 9√2, 12√2, 18, 14√2, 32√2, 46, 55√2, 64√2, 110, 110√2, 156, 142√2, 220, 174√2, 284.
Code: 2847 0 394 2203 284 174 1102 394 284 1101 394 394 1426 252 142 646 0 110 1567 64 174 1740 220 174 324 252 142 552 55 55 90 55 55 463 46 0 187 46 46 146 50 32 46 46 28 85 50 24 45 46 24 122 58 12 121 58 24 62 64 18
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)