Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:364AJ GHM
Order: 20
Horizontal side: 364 Vertical side: 364
Elements: 6, 6√2, 12, 9√2, 18, 16√2, 18√2, 32, 27√2, 64, 86, 64√2, 67√2, 128, 134, 99√2, 166, 198, 150√2, 182√2.
Code: 1985 0 166 1824 182 182 1506 214 214 323 214 182 865 214 128 164 198 166 276 187 155 1665 0 0 994 99 67 90 187 155 123 178 134 187 178 146 180 196 146 676 99 67 1345 166 0 64 172 128 63 178 128 1281 300 128 642 364 64 643 364 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)