Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:368AU GHM
Order: 20
Horizontal side: 368 Vertical side: 368
Elements: 4, 4√2, 12√2, 24, 24√2, 48, 43√2, 47√2, 48√2, 86, 90, 94, 96, 86√2, 94√2, 96√2, 180, 184, 188, 184√2.
Code: 1885 0 180 1844 184 184 1843 368 184 44 188 180 43 192 180 862 278 98 861 278 184 432 321 141 901 368 184 1805 0 0 964 96 84 963 192 84 470 321 141 940 274 94 941 368 94 484 144 36 483 192 36 244 168 12 243 192 12 124 180 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)