Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:340AA GHM
Order: 20
Horizontal side: 340 Vertical side: 340
Elements: 13√2, 26, 22√2, 26√2, 50, 53, 50√2, 53√2, 78, 96, 100, 103, 78√2, 122, 87√2, 96√2, 109√2, 166, 122√2, 131√2.
Code: 1312 131 209 1094 109 231 876 131 253 1227 218 340 1226 218 218 226 109 231 1005 131 153 262 244 192 536 78 156 263 244 166 962 340 96 134 231 153 1663 244 0 786 0 78 535 78 103 505 131 103 504 181 103 1037 78 103 963 340 0 785 0 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)