Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:366AE GHM
Order: 20
Horizontal side: 366 Vertical side: 366
Elements: 3√2, 14, 14√2, 20, 28, 26√2, 28√2, 72, 62√2, 98, 72√2, 108, 124, 98√2, 144, 150, 108√2, 134√2, 196, 147√2.
Code: 1505 0 216 1474 147 219 1443 294 222 722 366 294 721 366 366 1963 366 98 36 147 219 207 150 222 626 108 160 1247 170 222 1082 108 108 1081 108 216 282 136 188 281 136 216 142 150 202 141 150 216 262 134 134 1340 134 134 984 268 0 983 366 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)