Primitive Perfect Isosceles Right Triangled Square
Title: e 20:385AD GHM
Order: 20
Horizontal side: 385 Vertical side: 385
Elements: 20, 20√2, 36, 40, 30√2, 36√2, 54, 60, 72, 54√2, 60√2, 90, 72√2, 126, 90√2, 144, 115√2, 135√2, 205, 295.
Code: 2957 0 385 1156 180 270 907 295 385 906 295 295 602 355 235 1443 180 126 1352 315 135 603 355 175 302 385 205 2053 385 0 207 295 175 206 295 155 407 315 175 366 0 90 725 36 54 724 108 54 1263 180 0 365 0 54 545 0 0 544 54 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)