Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:328BT GHM
Order: 20
Horizontal side: 328 Vertical side: 328
Elements: 1√2, 2, 2√2, 4, 6, 7√2, 10√2, 14√2, 24√2, 34, 48, 82, 58√2, 82√2, 116, 130, 164, 116√2, 212, 164√2.
Code: 2125 0 116 1644 164 164 1643 328 164 481 212 164 345 212 130 584 270 106 826 246 82 72 219 123 61 218 130 45 218 126 144 232 116 1303 246 0 242 270 106 25 218 124 24 220 124 100 222 126 14 219 123 1165 0 0 1164 116 0 825 246 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)