Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:392AA GHM
Order: 20
Horizontal side: 392 Vertical side: 392
Elements: 19, 21√2, 42, 42√2, 60, 76, 57√2, 95, 68√2, 76√2, 114, 120, 128, 93√2, 136, 120√2, 128√2, 188, 136√2, 204.
Code: 1365 0 256 1364 136 256 2043 272 188 1207 272 392 1206 272 272 422 314 230 1282 128 128 684 68 188 423 314 188 212 335 209 1143 335 95 572 392 152 601 128 188 1885 128 0 934 221 95 766 316 76 1283 128 0 951 316 95 197 316 95 765 316 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)