Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:366AF GHM
Order: 20
Horizontal side: 366 Vertical side: 366
Elements: 22, 22√2, 24√2, 44, 33√2, 48, 44√2, 48√2, 78, 106, 78√2, 116, 134, 101√2, 144, 106√2, 154, 116√2, 130√2, 144√2.
Code: 1545 0 212 1304 130 236 1060 260 366 1061 366 366 246 130 236 485 154 212 484 202 212 1160 250 260 1161 366 260 1345 0 78 1014 101 111 336 101 111 445 134 100 444 178 100 1440 222 144 1441 366 144 225 134 78 224 156 78 785 0 0 784 78 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)