Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:390AC GHM
Order: 20
Horizontal side: 390 Vertical side: 390
Elements: 43, 36√2, 53, 64, 72, 82, 64√2, 96, 113, 80√2, 82√2, 123, 128, 96√2, 144, 154, 113√2, 164, 123√2, 154√2.
Code: 1545 0 236 1544 154 236 820 308 390 821 390 390 723 226 236 362 262 272 1641 390 308 966 166 176 1285 262 144 1135 0 123 1134 113 123 533 166 123 965 166 80 645 262 80 644 326 80 1443 390 0 1237 0 123 1230 123 123 431 166 123 804 246 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)