Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:328AQ GHM
Order: 20
Horizontal side: 328 Vertical side: 328
Elements: 8√2, 16, 16√2, 28, 32, 48, 54, 40√2, 41√2, 64, 54√2, 56√2, 82, 110, 80√2, 82√2, 136, 123√2, 192, 164√2.
Code: 1925 0 136 1644 164 164 1236 205 205 410 205 205 281 192 164 542 246 110 541 246 164 822 328 82 1365 0 0 804 80 56 166 144 120 327 160 136 406 152 96 643 144 56 165 144 104 1103 246 0 485 144 56 84 152 96 823 328 0 564 136 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)