Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:340AP GHM
Order: 20
Horizontal side: 340 Vertical side: 340
Elements: 4√2, 8, 8√2, 12, 14, 12√2, 24, 25√2, 28√2, 32√2, 53√2, 78, 92, 78√2, 92√2, 156, 170, 124√2, 184, 170√2.
Code: 1845 0 156 1704 170 170 1703 340 170 141 184 170 252 209 145 784 262 92 783 340 92 1567 0 156 326 124 124 85 156 148 84 164 148 120 172 156 121 184 156 282 184 120 44 160 144 530 209 145 241 184 144 1240 124 124 924 248 0 923 340 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)