Primitive Perfect Isosceles Right Triangled Square
Title: e 20:329AA3of8 GHM
Order: 20
Horizontal side: 329 Vertical side: 329
Elements: 8√2, 16, 16√2, 28, 32, 24√2, 28√2, 48, 56, 66, 47√2, 56√2, 66√2, 94, 122, 94√2, 141, 160, 141√2, 235.
Code: 2357 0 329 476 188 282 947 235 329 946 235 235 1603 188 122 1412 329 141 1413 329 0 286 0 94 565 28 66 481 76 122 242 100 98 564 132 66 1223 188 0 166 84 82 325 100 66 285 0 66 86 76 74 165 84 66 665 0 0 664 66 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)