Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:328CA1of2 GHM
Order: 20
Horizontal side: 328 Vertical side: 328
Elements: 3√2, 5, 8√2, 16, 16√2, 32, 24√2, 53, 54, 55, 56, 54√2, 55√2, 108, 109, 111, 111√2, 164, 217, 164√2.
Code: 2175 0 111 1644 164 164 1643 328 164 531 217 164 242 241 140 561 273 164 552 328 109 551 328 164 166 225 124 325 241 108 86 217 116 165 225 108 55 217 111 1115 0 0 1114 111 0 30 222 111 1093 328 0 1083 219 0 542 273 54 541 273 108
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)