Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:392AB GHM
Order: 20
Horizontal side: 392 Vertical side: 392
Elements: 2√2, 30, 30√2, 64, 61√2, 64√2, 96, 100, 74√2, 122, 128, 94√2, 96√2, 98√2, 100√2, 148, 109√2, 170, 122√2, 148√2.
Code: 1485 0 244 1484 148 244 1283 296 264 962 392 296 961 392 392 986 294 198 940 168 264 644 232 200 643 296 200 1222 122 122 744 74 170 304 262 170 303 292 170 1002 392 100 24 294 198 1094 183 61 1703 292 0 1223 122 0 612 183 61 1003 392 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)