Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:242AA GHM
Order: 20
Horizontal side: 242 Vertical side: 242
Elements: 16√2, 24, 17√2, 32, 24√2, 34, 32√2, 48, 34√2, 35√2, 68, 70, 72, 70√2, 100, 72√2, 102, 106, 85√2, 105√2.
Code: 1067 0 242 720 106 242 721 178 242 485 178 194 324 210 210 323 242 210 164 226 194 1056 137 105 245 178 170 244 202 170 346 0 136 687 34 170 856 17 85 1007 102 170 345 0 102 350 137 105 1025 0 0 174 17 85 707 102 70 700 172 70
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)