Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:292AA4of4 GHM
Order: 20
Horizontal side: 292 Vertical side: 292
Elements: 5√2, 16, 16√2, 28, 32, 28√2, 32√2, 48, 56, 66, 48√2, 56√2, 66√2, 94, 122, 132, 94√2, 99√2, 104√2, 132√2.
Code: 1325 0 160 1324 132 160 280 264 292 281 292 292 486 188 216 562 292 208 561 292 264 1223 188 94 485 188 168 1046 188 104 322 220 136 321 220 168 162 236 152 161 236 168 665 0 94 664 66 94 52 193 99 990 193 99 945 0 0 944 94 0
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)