Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:242AJ2of8 GHM
Order: 20
Horizontal side: 242 Vertical side: 242
Elements: 1, 6√2, 12, 12√2, 24, 18√2, 36, 40, 41, 42, 40√2, 41√2, 42√2, 80, 81, 80√2, 120, 121, 122, 121√2.
Code: 1227 0 242 800 122 242 801 202 242 402 242 202 401 242 242 813 242 121 66 36 156 127 42 162 126 42 150 247 54 162 420 78 162 421 120 162 415 120 121 414 161 121 363 36 120 182 54 138 17 120 121 1210 121 121 1211 242 121 1207 0 120
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)