Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:294AM GHM
Order: 20
Horizontal side: 294 Vertical side: 294
Elements: 2, 2√2, 4, 4√2, 6√2, 10, 8√2, 20, 24√2, 34, 48, 41√2, 48√2, 82, 82√2, 116, 130, 123√2, 130√2, 212.
Code: 2127 0 294 480 212 294 481 260 294 242 284 270 341 294 294 46 280 266 105 284 260 203 280 246 45 280 262 82 288 254 24 282 260 23 284 260 64 288 254 1306 164 130 1236 41 123 1167 164 246 1305 164 0 410 41 123 827 0 82 820 82 82
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)