Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:392AF GHM
Order: 20
Horizontal side: 392 Vertical side: 392
Elements: 2, 2√2, 4, 4√2, 8, 8√2, 16, 46, 46√2, 92, 77√2, 116, 85√2, 92√2, 138, 116√2, 184, 138√2, 230, 254.
Code: 2547 0 392 920 254 392 921 346 392 462 392 346 461 392 392 2303 392 116 856 77 215 1847 162 300 770 77 215 1387 0 138 1380 138 138 161 154 138 82 162 130 83 162 122 44 158 118 43 162 118 24 160 116 23 162 116 1164 276 0 1163 392 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)