Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:296AD1of2 GHM
Order: 20
Horizontal side: 296 Vertical side: 296
Elements: 8, 8√2, 16, 16√2, 28, 32, 23√2, 28√2, 32√2, 46, 37√2, 46√2, 74, 56√2, 74√2, 120, 148, 111√2, 125√2, 148√2.
Code: 1482 148 148 1254 125 171 460 250 296 461 296 296 560 204 250 324 236 218 323 268 218 282 296 222 281 296 250 1483 296 74 164 252 202 163 268 202 84 260 194 83 268 194 236 125 171 1207 148 194 376 111 111 1110 111 111 744 222 0 743 296 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)