Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:340AR GHM
Order: 20
Horizontal side: 340 Vertical side: 340
Elements: 6, 6√2, 12, 16, 18, 16√2, 32, 29√2, 42, 32√2, 64, 76, 94, 76√2, 94√2, 152, 170, 123√2, 188, 170√2.
Code: 1885 0 152 1704 170 170 1703 340 170 181 188 170 125 188 158 764 264 94 763 340 94 65 188 152 64 194 152 326 168 126 645 200 94 1527 0 152 296 123 123 427 152 152 166 152 110 325 168 94 1230 123 123 165 152 94 944 246 0 943 340 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)