Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:386AB1of2 GHM
Order: 20
Horizontal side: 386 Vertical side: 386
Elements: 16√2, 24, 32, 24√2, 44, 32√2, 48, 44√2, 64, 70, 72, 57√2, 88, 70√2, 114, 158, 114√2, 158√2, 171√2, 272.
Code: 2727 0 386 576 215 329 1147 272 386 1146 272 272 1710 215 329 446 0 114 887 44 158 166 116 142 327 132 158 326 132 126 647 164 158 1580 228 158 1581 386 158 723 116 70 485 116 94 445 0 70 245 116 70 244 140 70 705 0 0 704 70 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)