Primitive Perfect Isosceles Right Triangled Square
Title: __ 19:172AF GHM
Order: 19
Horizontal side: 172 Vertical side: 172
Elements: 3, 3√2, 13√2, 14√2, 26, 28, 25√2, 26√2, 28√2, 50, 39√2, 58, 42√2, 50√2, 72, 75, 58√2, 61√2, 72√2.
Code: 725 0 100 724 72 100 146 130 158 287 144 172 286 144 144 420 130 158 136 75 103 267 88 116 266 88 90 587 114 116 586 114 58 33 75 100 392 114 64 502 50 50 751 75 100 36 111 61 610 111 61 503 50 0 252 75 25
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)