Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:462AA GHM
Order: 20
Horizontal side: 462 Vertical side: 462
Elements: 6√2, 12, 12√2, 24, 24√2, 48, 47√2, 48√2, 90, 94, 90√2, 92√2, 94√2, 184, 186, 188, 139√2, 182√2, 184√2, 186√2.
Code: 1862 186 276 1394 139 323 926 186 370 1847 278 462 1846 278 278 476 139 323 1822 368 188 1863 186 90 1883 368 0 942 462 94 943 462 0 907 0 90 900 90 90 484 138 42 483 186 42 244 162 18 243 186 18 124 174 6 123 186 6 64 180 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)