Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:264AR GHM
Order: 20
Horizontal side: 264 Vertical side: 264
Elements: 5√2, 10, 14, 10√2, 15, 14√2, 15√2, 30, 45, 52, 66, 52√2, 80, 59√2, 66√2, 80√2, 118, 132, 146, 132√2.
Code: 1467 0 264 596 87 205 1187 146 264 1326 132 132 303 87 175 455 87 160 50 57 175 154 72 160 153 87 160 526 0 118 107 52 170 100 62 170 807 52 160 806 52 80 142 146 146 1325 132 0 525 0 66 145 52 66 667 0 66 660 66 66
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)