Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:91AD GHM
Order: 20
Horizontal side: 91 Vertical side: 91
Elements: 1√2, 2, 2√2, 4, 6, 5√2, 7√2, 10, 10√2, 20, 24, 17√2, 30, 22√2, 37, 27√2, 44, 47, 37√2, 54.
Code: 545 0 37 441 44 91 305 44 61 471 91 91 72 51 54 61 50 61 45 50 57 241 74 61 172 91 44 25 50 55 24 52 55 106 44 47 205 54 37 14 51 54 226 69 22 375 0 0 374 37 0 103 74 27 270 64 27 54 69 22
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)