Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:366AK GHM
Order: 20
Horizontal side: 366 Vertical side: 366
Elements: 12√2, 20, 19√2, 20√2, 40, 40√2, 60√2, 90, 100, 76√2, 114, 90√2, 95√2, 138, 140, 100√2, 152, 114√2, 176, 138√2.
Code: 1767 0 366 1000 176 366 1001 276 366 902 366 276 901 366 366 1386 228 138 766 0 190 1525 76 114 1401 216 266 207 216 266 206 216 246 407 236 266 406 236 226 602 276 186 952 95 95 126 216 126 1385 228 0 194 95 95 1140 114 114 1141 228 114
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)