Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:456AJ GHM
Order: 20
Horizontal side: 456 Vertical side: 456
Elements: 2√2, 4, 4√2, 6, 6√2, 12, 18, 32, 32√2, 50, 64, 57√2, 114, 114√2, 164, 178, 164√2, 171√2, 292, 228√2.
Code: 2925 0 164 2284 228 228 1716 285 285 570 285 285 641 292 228 322 324 196 501 342 228 1142 456 114 323 324 164 185 324 178 67 324 178 66 324 172 127 330 178 1783 342 0 42 328 168 43 328 164 22 330 166 1645 0 0 1644 164 0 1143 456 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)