Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:452AA GHM
Order: 20
Horizontal side: 452 Vertical side: 452
Elements: 3√2, 12, 12√2, 24, 36, 36√2, 72, 88, 94, 72√2, 88√2, 138, 176, 182, 132√2, 188, 135√2, 138√2, 176√2, 182√2.
Code: 1887 0 452 1760 188 452 1761 364 452 882 452 364 881 452 452 1826 270 182 120 12 276 121 24 276 367 24 276 366 24 240 727 60 276 726 60 204 1387 132 276 1386 132 138 947 270 276 1322 132 132 241 24 264 1825 270 0 32 135 135 1350 135 135
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)