Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:390AI GHM
Order: 20
Horizontal side: 390 Vertical side: 390
Elements: 20, 20√2, 36, 40, 30√2, 60, 53√2, 60√2, 88, 106, 124, 88√2, 89√2, 140, 142, 106√2, 124√2, 178, 142√2, 160√2.
Code: 1787 0 390 880 178 390 881 266 390 1247 266 390 1246 266 266 606 30 242 1407 90 302 1600 230 302 361 266 302 306 0 212 605 30 182 1062 106 106 401 70 182 202 90 162 201 90 182 894 159 53 1420 248 142 1421 390 142 1063 106 0 532 159 53
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)