Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:364AU GHM
Order: 20
Horizontal side: 364 Vertical side: 364
Elements: 6√2, 12, 12√2, 24, 36, 40, 42, 31√2, 40√2, 42√2, 62, 78, 80, 80√2, 142, 102√2, 111√2, 142√2, 222, 182√2.
Code: 2225 0 142 1824 182 182 1026 262 262 803 262 182 785 262 184 427 262 184 420 304 184 361 340 184 245 340 160 404 222 142 403 262 142 125 340 148 124 352 148 806 284 80 64 346 142 1425 0 0 1424 142 0 316 253 111 627 284 142 1110 253 111
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)