Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:366AJ GHM
Order: 20
Horizontal side: 366 Vertical side: 366
Elements: 12√2, 24, 24√2, 36, 48, 47√2, 72, 84, 94, 68√2, 78√2, 84√2, 126, 94√2, 136, 110√2, 162, 115√2, 188, 136√2.
Code: 1625 0 204 1154 115 251 686 162 298 1367 230 366 1366 230 230 476 115 251 1102 272 188 367 0 204 246 12 180 485 36 156 1261 162 204 1883 272 0 942 366 94 126 0 168 245 12 156 842 84 84 721 84 156 782 162 78 943 366 0 843 84 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)