Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:242AK4of8 GHM
Order: 20
Horizontal side: 242 Vertical side: 242
Elements: 6√2, 12, 12√2, 21, 24, 18√2, 20√2, 21√2, 36, 40, 42, 40√2, 42√2, 61, 80, 80√2, 120, 122, 101√2, 121√2.
Code: 1227 0 242 800 122 242 801 202 242 402 242 202 401 242 242 1016 141 101 243 42 138 367 42 162 420 78 162 421 120 162 212 141 141 211 141 162 617 141 162 206 121 121 180 18 138 124 30 126 123 42 126 64 36 120 1210 121 121 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)