Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:366AG GHM
Order: 20
Horizontal side: 366 Vertical side: 366
Elements: 24, 17√2, 24√2, 48, 40√2, 80, 86, 65√2, 92, 106, 80√2, 120, 86√2, 89√2, 126, 106√2, 154, 120√2, 123√2, 140√2.
Code: 1547 0 366 896 65 277 867 154 366 860 240 366 1261 366 366 927 154 280 1406 106 140 802 326 200 801 326 280 402 366 240 650 65 277 1206 246 120 1062 106 106 1061 106 212 247 106 212 240 130 212 487 106 188 172 123 123 1230 123 123 1205 246 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)