Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:166AU4of8 GHM
Order: 20
Horizontal side: 166 Vertical side: 166
Elements: 1, 1√2, 2, 2√2, 3, 4, 5, 5√2, 19, 19√2, 38, 52, 38√2, 57, 71, 52√2, 76, 57√2, 95, 109.
Code: 1097 0 166 713 109 95 577 109 166 576 109 109 45 109 105 52 114 100 31 112 105 17 112 105 10 113 105 27 112 104 26 112 102 522 166 52 53 114 95 386 0 57 767 38 95 953 114 0 385 0 19 523 166 0 195 0 0 194 19 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)