Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:328BG2of2 GHM
Order: 20
Horizontal side: 328 Vertical side: 328
Elements: 2√2, 4, 4√2, 13√2, 26, 28, 20√2, 32, 26√2, 40, 32√2, 46√2, 72, 92, 118, 105√2, 164, 118√2, 210, 164√2.
Code: 2105 0 118 1644 164 164 1643 328 164 464 210 118 206 236 144 405 256 124 721 328 164 263 236 118 262 262 118 44 260 120 43 264 120 327 264 124 320 296 124 24 262 118 283 264 92 1185 0 0 1184 118 0 136 223 105 1050 223 105 921 328 92
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)