Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:456AS GHM
Order: 20
Horizontal side: 456 Vertical side: 456
Elements: 2√2, 4, 4√2, 8, 12, 14, 14√2, 28, 21√2, 42, 55√2, 110, 152, 110√2, 173, 194, 152√2, 173√2, 283, 304.
Code: 3045 0 152 2831 283 456 1737 283 456 1736 283 283 552 338 228 46 334 224 85 338 220 26 332 222 45 334 220 283 332 194 142 346 208 121 346 220 1102 456 110 143 346 194 216 283 173 427 304 194 1943 346 0 1525 0 0 1524 152 0 1103 456 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)