Primitive Perfect Isosceles Right Triangled Square
Title: d 20:365AA GHM
Order: 20
Horizontal side: 365 Vertical side: 365
Elements: 22, 22√2, 38√2, 48√2, 74, 76, 96, 99, 107, 76√2, 114, 122, 129, 96√2, 137, 99√2, 144, 107√2, 114√2, 129√2.
Code: 1377 0 365 990 137 365 991 236 365 1297 236 365 1296 236 236 386 0 228 767 38 266 766 38 190 1227 114 266 743 236 192 222 258 214 1142 114 114 223 258 192 1072 365 107 486 114 144 967 162 192 966 162 96 1445 114 0 1143 114 0 1073 365 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)