Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:340AC GHM
Order: 20
Horizontal side: 340 Vertical side: 340
Elements: 16, 16√2, 32, 23√2, 48, 64, 66, 68, 90, 92, 68√2, 112, 80√2, 114, 90√2, 136, 113√2, 160, 114√2, 136√2.
Code: 1362 136 204 1134 113 227 906 136 250 1147 226 340 1146 226 226 236 113 227 905 136 160 665 226 160 1363 136 68 927 136 160 1603 228 0 802 308 80 641 292 160 485 292 112 167 292 112 166 292 96 327 308 112 1123 340 0 685 0 0 684 68 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)