Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:127AG1of2 GHM
Order: 20
Horizontal side: 127 Vertical side: 127
Elements: 4, 4√2, 8, 8√2, 12, 14, 16, 14√2, 20, 28, 21√2, 36, 28√2, 42, 43, 56, 42√2, 43√2, 70, 85.
Code: 857 0 127 280 85 127 281 113 127 142 127 113 141 127 127 703 127 43 363 57 63 567 57 99 210 21 63 121 33 63 47 33 63 40 37 63 201 57 63 87 33 59 86 33 51 165 41 43 434 84 0 433 127 0 427 0 42 420 42 42
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)