Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:388AA GHM
Order: 20
Horizontal side: 388 Vertical side: 388
Elements: 24, 24√2, 38, 31√2, 54, 56, 52√2, 54√2, 55√2, 86, 62√2, 70√2, 104, 108, 124, 104√2, 156, 132√2, 232, 194√2.
Code: 2325 0 156 1944 194 194 1326 256 256 620 256 256 381 232 194 312 263 163 861 318 194 702 388 124 550 263 163 1565 0 0 1044 104 52 1043 208 52 242 232 132 241 232 156 1243 388 0 567 208 108 1083 264 0 542 318 54 541 318 108 524 156 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)