Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:462AD GHM
Order: 20
Horizontal side: 462 Vertical side: 462
Elements: 16, 18, 16√2, 18√2, 36, 38√2, 54, 60, 72, 74, 60√2, 67√2, 104, 134, 104√2, 134√2, 194, 194√2, 201√2, 328.
Code: 3287 0 462 676 261 395 1347 328 462 1346 328 328 2010 261 395 606 0 134 1045 60 90 1044 164 90 1940 268 194 1941 462 194 605 0 74 165 60 74 164 76 74 543 92 36 727 92 90 745 0 0 384 38 36 361 74 36 182 92 18 181 92 36
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)