Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:366AD GHM
Order: 20
Horizontal side: 366 Vertical side: 366
Elements: 3√2, 14, 14√2, 20, 28, 21√2, 28√2, 72, 62√2, 98, 72√2, 108, 124, 98√2, 144, 108√2, 160, 129√2, 196, 147√2.
Code: 1472 147 219 1294 129 237 1080 258 366 1081 366 366 216 129 237 285 150 230 284 178 230 620 206 258 1601 366 258 145 150 216 144 164 216 30 147 219 1443 144 72 207 144 216 1247 144 196 1963 268 0 982 366 98 983 366 0 725 0 0 724 72 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)