Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:368AO GHM
Order: 20
Horizontal side: 368 Vertical side: 368
Elements: 1√2, 18√2, 36, 40, 36√2, 54, 40√2, 54√2, 80, 82, 108, 80√2, 82√2, 122, 124, 164, 122√2, 123√2, 124√2, 164√2.
Code: 1645 0 204 1644 164 204 400 328 368 401 368 368 800 288 328 801 368 328 186 190 230 367 208 248 366 208 212 1247 244 248 1246 244 124 1083 190 122 542 244 176 825 0 122 824 82 122 543 244 122 12 245 123 1230 245 123 1225 0 0 1224 122 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)