Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:460AE GHM
Order: 20
Horizontal side: 460 Vertical side: 460
Elements: 20√2, 24√2, 25√2, 40, 48, 50, 36√2, 48√2, 72, 90, 96, 84√2, 90√2, 96√2, 115√2, 180, 140√2, 230, 280, 230√2.
Code: 2805 0 180 2304 230 230 2303 460 230 501 280 230 905 280 140 904 370 140 1156 345 115 1805 0 0 964 96 84 963 192 84 482 240 132 481 240 180 242 264 156 401 280 180 723 264 84 362 300 120 204 300 120 1400 320 140 254 345 115 844 180 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)