Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:382AA GHM
Order: 20
Horizontal side: 382 Vertical side: 382
Elements: 4√2, 36√2, 38√2, 68, 72, 76, 68√2, 70√2, 72√2, 106, 76√2, 114, 122, 130, 138, 146, 122√2, 126√2, 130√2, 138√2.
Code: 1385 0 244 1384 138 244 700 276 382 1061 382 382 680 206 312 681 274 312 722 346 240 721 346 312 362 382 276 1463 382 130 1222 122 122 1221 122 244 1145 122 130 764 198 168 763 274 168 384 236 130 42 126 126 1304 252 0 1303 382 0 1260 126 126
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)