Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:460AD GHM
Order: 20
Horizontal side: 460 Vertical side: 460
Elements: 16√2, 32, 36, 32√2, 64, 64√2, 92, 73√2, 74√2, 112, 128, 92√2, 146, 128√2, 129√2, 130√2, 184, 202, 258, 184√2.
Code: 2585 0 202 1844 184 276 1843 368 276 922 460 368 921 460 460 1286 332 240 744 258 202 1306 202 146 367 332 276 1285 332 112 2025 0 0 1294 129 73 736 129 73 1465 202 0 645 332 48 644 396 48 1123 460 0 325 332 16 324 364 16 164 348 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)