Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:328BA GHM
Order: 20
Horizontal side: 328 Vertical side: 328
Elements: 2√2, 6√2, 8√2, 12, 14, 10√2, 16, 20, 16√2, 23√2, 36, 46, 82, 82√2, 118, 105√2, 164, 118√2, 210, 164√2.
Code: 2105 0 118 1644 164 164 1643 328 164 461 210 164 162 226 148 361 246 164 827 246 164 826 246 82 163 226 132 205 226 128 145 210 118 84 218 124 26 224 130 66 218 124 125 224 118 104 236 118 236 223 105 1185 0 0 1184 118 0 1050 223 105
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)