Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:456AM GHM
Order: 20
Horizontal side: 456 Vertical side: 456
Elements: 2√2, 4, 4√2, 8, 8√2, 14, 14√2, 15√2, 28, 42, 36√2, 57√2, 114, 156, 114√2, 150√2, 156√2, 228, 300, 228√2.
Code: 3005 0 156 2284 228 228 2283 456 228 574 285 171 423 342 186 1147 342 228 1146 342 114 156 285 171 147 300 186 146 300 172 287 314 186 366 306 150 82 308 164 83 308 156 42 312 160 43 312 156 22 314 158 1565 0 0 1564 156 0 1500 306 150
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)