Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:292AE GHM
Order: 20
Horizontal side: 292 Vertical side: 292
Elements: 2√2, 4, 4√2, 6√2, 26, 34, 26√2, 34√2, 40√2, 60, 43√2, 72, 80, 86, 80√2, 120, 86√2, 103√2, 172, 146√2.
Code: 1725 0 120 1464 146 146 1036 189 189 430 189 189 264 172 120 340 198 146 341 232 146 605 232 86 1205 0 0 804 80 40 803 160 40 42 164 116 64 166 114 43 164 112 22 166 114 727 160 112 263 232 86 860 206 86 861 292 86 404 120 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)