Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:342AA GHM
Order: 20
Horizontal side: 342 Vertical side: 342
Elements: 6, 6√2, 12, 18, 18√2, 36, 35√2, 36√2, 66, 70, 66√2, 68√2, 70√2, 136, 138, 140, 103√2, 134√2, 136√2, 138√2.
Code: 1382 138 204 1034 103 239 686 138 274 1367 206 342 1366 206 206 356 103 239 1342 272 140 1383 138 66 1403 272 0 702 342 70 703 342 0 667 0 66 660 66 66 364 102 30 363 138 30 184 120 12 183 138 12 121 132 12 62 138 6 61 138 12
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)