Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:394AB GHM
Order: 20
Horizontal side: 394 Vertical side: 394
Elements: 23√2, 36, 34√2, 36√2, 68, 92, 68√2, 100, 82√2, 118, 84√2, 128, 92√2, 138, 100√2, 105√2, 174, 128√2, 184, 138√2.
Code: 1385 0 256 1384 138 256 340 276 394 1181 394 394 680 242 360 681 310 360 842 394 276 360 174 292 361 210 292 1002 310 192 1001 310 292 1843 394 92 1282 128 128 1054 105 151 826 128 174 236 105 151 1745 128 0 1283 128 0 924 302 0 923 394 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)