Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:264AF4of8 GHM
Order: 20
Horizontal side: 264 Vertical side: 264
Elements: 8√2, 16, 16√2, 28, 32, 24√2, 28√2, 33√2, 48, 38√2, 56, 66, 47√2, 66√2, 94, 104, 85√2, 132, 99√2, 132√2.
Code: 1322 132 132 994 99 165 660 198 264 661 264 264 336 99 165 1327 132 198 1043 264 94 476 85 85 286 132 66 567 160 94 323 216 62 487 216 94 943 264 0 850 85 85 285 132 38 240 184 62 164 200 46 163 216 46 84 208 38 384 170 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)