Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:392AD GHM
Order: 20
Horizontal side: 392 Vertical side: 392
Elements: 6, 7√2, 14, 16, 14√2, 22, 21√2, 22√2, 28√2, 44, 60, 76, 60√2, 120, 152, 120√2, 136√2, 152√2, 240, 196√2.
Code: 2405 0 152 1964 196 196 1366 256 256 603 256 196 765 256 180 441 240 196 222 262 174 161 256 196 61 262 180 142 276 166 141 276 180 72 283 173 284 304 152 600 332 180 223 262 152 210 283 173 1525 0 0 1524 152 0 1200 272 120 1201 392 120
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)