Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:394AC GHM
Order: 20
Horizontal side: 394 Vertical side: 394
Elements: 23√2, 36, 34√2, 36√2, 59, 68, 92, 68√2, 100, 105, 118, 84√2, 92√2, 138, 100√2, 105√2, 128√2, 184, 138√2, 151√2.
Code: 1512 151 243 1284 128 266 1056 151 289 1387 256 394 1386 256 256 236 128 266 1055 151 184 362 292 220 593 151 184 363 292 184 682 360 152 926 0 92 1845 92 0 1004 192 84 1003 292 84 683 360 84 342 394 118 1183 394 0 925 0 0 844 276 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)