Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:224AC GHM
Order: 20
Horizontal side: 224 Vertical side: 224
Elements: 12, 12√2, 32, 28√2, 40, 44, 32√2, 33√2, 40√2, 44√2, 46√2, 66, 72, 53√2, 86, 92, 66√2, 72√2, 106, 92√2.
Code: 925 0 132 924 92 132 326 152 192 407 184 224 406 184 184 1063 152 86 325 152 160 122 196 172 123 196 160 282 224 144 442 196 116 441 196 160 726 152 72 662 66 66 464 46 86 534 99 33 863 152 0 725 152 0 663 66 0 332 99 33
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)