Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:264AV GHM
Order: 20
Horizontal side: 264 Vertical side: 264
Elements: 6√2, 12, 12√2, 13√2, 18√2, 26, 20√2, 36, 46, 33√2, 60, 66, 72, 56√2, 66√2, 112, 86√2, 132, 152, 132√2.
Code: 1527 0 264 723 152 192 467 152 264 336 165 231 667 198 264 666 198 198 130 165 231 267 152 218 860 178 218 66 74 186 127 80 192 126 80 180 607 92 192 180 74 186 560 56 168 361 92 168 204 112 112 1320 132 132 1321 264 132 1127 0 112
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)