Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:294AD GHM
Order: 20
Horizontal side: 294 Vertical side: 294
Elements: 4√2, 8, 9, 8√2, 12, 12√2, 14√2, 24, 23√2, 28√2, 46, 55, 46√2, 92, 110, 92√2, 101√2, 110√2, 184, 147√2.
Code: 1845 0 110 1474 147 147 1016 193 193 463 193 147 555 193 138 234 170 124 93 193 138 146 170 124 82 192 130 81 192 138 42 196 134 284 220 110 460 248 138 126 184 122 245 196 110 125 184 110 1105 0 0 1104 110 0 920 202 92 921 294 92
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)