Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:392AC GHM
Order: 20
Horizontal side: 392 Vertical side: 392
Elements: 19, 21√2, 42, 30√2, 42√2, 60, 76, 57√2, 95, 68√2, 76√2, 114, 120, 93√2, 136, 120√2, 128√2, 136√2, 204, 158√2.
Code: 1582 158 234 1284 128 264 686 188 324 1367 256 392 1366 256 256 603 188 264 2045 188 120 304 158 234 936 95 171 953 95 76 1145 95 57 425 188 78 424 230 78 1200 272 120 1201 392 120 214 209 57 767 0 76 760 76 76 191 95 76 574 152 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)