Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:364AN GHM
Order: 20
Horizontal side: 364 Vertical side: 364
Elements: 3√2, 6, 6√2, 12, 18, 20√2, 21√2, 40, 30√2, 60, 80, 61√2, 80√2, 122, 142, 101√2, 162, 142√2, 202, 182√2.
Code: 2025 0 162 1824 182 182 1426 222 222 403 222 182 1425 222 80 204 202 162 603 222 122 1625 0 0 1014 101 61 616 101 61 1225 162 0 304 192 92 216 201 101 30 201 101 60 198 98 61 204 98 185 204 80 121 204 92 804 284 0 803 364 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)