Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:328AO GHM
Order: 20
Horizontal side: 328 Vertical side: 328
Elements: 8, 8√2, 16, 18, 24, 18√2, 23√2, 36, 28√2, 46, 54, 70, 94, 70√2, 94√2, 140, 164, 117√2, 188, 164√2.
Code: 1885 0 140 1644 164 164 1643 328 164 241 188 164 165 188 148 704 258 94 703 328 94 85 188 140 84 196 140 363 204 112 545 204 94 1407 0 140 236 117 117 465 140 94 284 168 112 1170 117 117 184 186 94 183 204 94 944 234 0 943 328 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)