Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:312AA1of2 GHM
Order: 20
Horizontal side: 312 Vertical side: 312
Elements: 8√2, 16, 16√2, 24, 28, 24√2, 28√2, 48, 39√2, 50√2, 53√2, 78, 56√2, 106, 78√2, 128, 103√2, 156, 117√2, 156√2.
Code: 1562 156 156 1174 117 195 780 234 312 781 312 312 396 117 195 1567 156 234 1283 312 106 536 103 103 286 156 78 162 200 90 161 200 106 82 208 98 564 256 50 1063 312 0 1030 103 103 246 184 74 485 208 50 285 156 50 245 184 50 504 206 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)