Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:368AB GHM
Order: 20
Horizontal side: 368 Vertical side: 368
Elements: 17√2, 26, 36, 26√2, 36√2, 52, 72, 52√2, 72√2, 74√2, 110, 78√2, 112, 146, 148, 108√2, 110√2, 112√2, 129√2, 148√2.
Code: 1485 0 220 1484 148 220 366 260 332 727 296 368 726 296 296 1080 260 332 780 152 224 524 204 172 523 256 172 1127 256 224 1126 256 112 1102 110 110 744 74 146 264 230 146 263 256 146 361 110 146 1467 110 146 176 239 129 1290 239 129 1103 110 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)