Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:456AI GHM
Order: 20
Horizontal side: 456 Vertical side: 456
Elements: 16√2, 32, 24√2, 32√2, 48, 54, 40√2, 60, 54√2, 56√2, 57√2, 112, 114, 112√2, 114√2, 168, 174, 171√2, 288, 228√2.
Code: 2885 0 168 2284 228 228 1716 285 285 570 285 285 601 288 228 542 342 174 541 342 228 1142 456 114 1743 342 0 1685 0 0 1124 112 56 1123 224 56 325 224 136 324 256 136 483 288 120 402 264 96 164 240 120 244 264 96 1143 456 0 564 168 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)