Primitive Perfect Isosceles Right Triangled Square
Title: __ 19:266AD GHM
Order: 19
Horizontal side: 266 Vertical side: 266
Elements: 2, 2√2, 4, 4√2, 8, 14, 16, 30, 22√2, 44, 37√2, 44√2, 74, 104, 74√2, 118, 111√2, 118√2, 192.
Code: 1927 0 266 440 192 266 441 236 266 222 258 244 301 266 266 46 254 240 85 258 236 26 252 238 45 254 236 163 252 222 25 252 236 147 252 236 1186 148 118 1116 37 111 1047 148 222 1185 148 0 370 37 111 747 0 74 740 74 74
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)