Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:384AB GHM
Order: 20
Horizontal side: 384 Vertical side: 384
Elements: 12, 14, 12√2, 22, 24, 21√2, 36, 42, 36√2, 46√2, 50√2, 92, 100, 92√2, 100√2, 142, 121√2, 142√2, 242, 192√2.
Code: 2425 0 142 1924 192 192 926 292 292 1003 292 192 925 292 200 225 292 178 464 338 154 1006 284 100 504 242 142 143 292 178 360 278 178 361 314 178 245 314 154 125 314 142 124 326 142 1425 0 0 1424 142 0 216 263 121 427 284 142 1210 263 121
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)