Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:368AR GHM
Order: 20
Horizontal side: 368 Vertical side: 368
Elements: 16√2, 32, 32√2, 39√2, 56, 64, 50√2, 78, 64√2, 67√2, 100, 106, 78√2, 112, 84√2, 128, 134, 128√2, 184, 184√2.
Code: 1845 0 184 1844 184 184 1286 240 240 563 240 184 1285 240 112 1067 0 184 676 39 117 1347 106 184 846 156 100 390 39 117 645 240 48 644 304 48 1123 368 0 506 106 50 1005 156 0 787 0 78 780 78 78 325 240 16 324 272 16 164 256 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)