Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:364AC GHM
Order: 20
Horizontal side: 364 Vertical side: 364
Elements: 7√2, 16√2, 32, 32√2, 38√2, 64, 76, 64√2, 100, 76√2, 114, 124, 126, 138, 140, 100√2, 112√2, 119√2, 124√2, 126√2.
Code: 1407 0 364 1240 140 364 1241 264 364 1002 364 264 1001 364 364 1383 364 126 166 0 224 327 16 240 326 16 208 647 48 240 646 48 176 1145 112 126 764 188 164 763 264 164 1122 112 112 384 226 126 72 119 119 1264 238 0 1263 364 0 1190 119 119
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)