Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:462AB GHM
Order: 20
Horizontal side: 462 Vertical side: 462
Elements: 2√2, 4, 4√2, 6√2, 10, 12, 10√2, 12√2, 20√2, 54, 54√2, 59√2, 118, 162, 118√2, 182, 162√2, 172√2, 300, 231√2.
Code: 3005 0 162 2314 231 231 1726 290 290 596 231 231 542 344 236 543 344 182 1182 462 118 107 290 182 106 290 172 42 304 178 41 304 182 22 306 180 204 324 162 1823 344 0 60 306 180 127 300 174 120 312 174 1625 0 0 1624 162 0 1183 462 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)