Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:342AN GHM
Order: 20
Horizontal side: 342 Vertical side: 342
Elements: 8, 10, 10√2, 12√2, 20, 22, 30, 22√2, 38, 27√2, 46, 76, 76√2, 114, 122, 144, 152, 114√2, 228, 171√2.
Code: 2285 0 114 1714 171 171 1443 342 198 276 171 171 222 220 176 221 220 198 465 220 152 1221 342 198 126 208 164 106 198 154 205 208 144 105 198 144 81 228 152 387 228 152 1523 266 0 762 342 76 301 228 144 1145 0 0 1144 114 0 763 342 0
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)