Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:264AQ GHM
Order: 20
Horizontal side: 264 Vertical side: 264
Elements: 8, 12, 12√2, 14√2, 20, 24, 28, 24√2, 28√2, 48, 42√2, 45√2, 84, 90, 73√2, 104, 118, 132, 146, 132√2.
Code: 1465 0 118 1324 132 132 1323 264 132 144 146 118 426 118 90 845 160 48 1041 264 132 1185 0 0 734 73 45 456 73 45 905 118 0 481 208 48 242 232 24 241 232 48 122 244 36 121 244 48 205 244 28 83 244 28 280 236 28 281 264 28
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)