Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:166AQ1of4 GHM
Order: 20
Horizontal side: 166 Vertical side: 166
Elements: 7, 5√2, 10, 10√2, 13√2, 19, 20, 15√2, 25, 19√2, 20√2, 25√2, 38, 51, 45√2, 64, 51√2, 64√2, 102, 83√2.
Code: 1025 0 64 834 83 83 456 121 121 383 121 83 152 136 106 50 136 106 100 131 101 101 141 101 252 166 76 207 121 91 206 121 71 194 102 64 193 121 64 253 166 51 75 121 64 645 0 0 644 64 0 130 128 64 510 115 51 511 166 51
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)