Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:272AA GHM
Order: 20
Horizontal side: 272 Vertical side: 272
Elements: 3√2, 6, 26√2, 42, 51, 52, 45√2, 47√2, 48√2, 52√2, 84, 89, 94, 96, 105, 78√2, 84√2, 89√2, 131, 94√2.
Code: 945 0 178 944 94 178 456 143 227 847 188 272 846 188 188 963 143 131 482 191 179 65 188 182 34 191 179 513 194 131 782 272 104 892 89 89 474 47 131 421 89 131 1315 89 0 1051 194 131 526 220 52 893 89 0 266 194 26 525 220 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)