Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:368AI GHM
Order: 20
Horizontal side: 368 Vertical side: 368
Elements: 15√2, 20√2, 30, 40, 40√2, 60, 76, 60√2, 104, 107, 76√2, 77√2, 124, 137, 140, 107√2, 152, 154, 124√2, 154√2.
Code: 1545 0 214 1544 154 214 1403 308 228 607 308 368 606 308 308 402 348 268 403 348 228 202 368 248 1246 244 124 760 168 228 761 244 228 1047 244 228 1072 107 107 774 77 137 150 92 152 1521 244 152 301 107 137 1375 107 0 1245 244 0 1073 107 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)