Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:382AD GHM
Order: 20
Horizontal side: 382 Vertical side: 382
Elements: 23√2, 46, 46√2, 52√2, 74, 78, 88, 92, 96, 104, 78√2, 134, 96√2, 138, 104√2, 148, 152, 156, 115√2, 152√2.
Code: 1525 0 230 1524 152 230 780 304 382 781 382 382 743 226 230 1042 330 200 1561 382 304 1152 115 115 921 92 230 462 138 184 1341 226 230 1043 330 96 522 382 148 463 138 138 885 138 96 1483 382 0 234 115 115 1383 138 0 965 138 0 964 234 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)