Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:464AC GHM
Order: 20
Horizontal side: 464 Vertical side: 464
Elements: 8√2, 16, 16√2, 32, 32√2, 56, 56√2, 65√2, 120, 130, 93√2, 102√2, 158, 168, 176, 130√2, 186, 204, 176√2, 204√2.
Code: 2045 0 260 2044 204 260 1203 408 344 567 408 464 566 408 408 322 440 376 323 440 344 162 456 360 163 456 344 82 464 352 1766 288 176 1863 288 158 1687 288 344 1302 130 130 1024 102 158 1765 288 0 934 195 65 1583 288 0 1303 130 0 652 195 65
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)