Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:256BI GHM
Order: 20
Horizontal side: 256 Vertical side: 256
Elements: 6, 6√2, 12, 12√2, 14√2, 15√2, 28, 30, 27√2, 56, 43√2, 47√2, 53√2, 56√2, 86, 71√2, 114, 100√2, 142, 128√2.
Code: 1425 0 114 1284 128 128 1006 156 156 283 156 128 472 203 109 144 142 114 276 129 101 1145 0 0 714 71 43 530 203 109 150 129 101 436 71 43 865 114 0 301 144 86 122 156 74 123 156 62 65 144 56 64 150 56 564 200 0 563 256 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)