Primitive Perfect Isosceles Right Triangled Square
Title: _r 19:124AA3of4 GHM
Order: 19
Horizontal side: 124 Vertical side: 124
Elements: 6, 6√2, 18, 13√2, 16√2, 26, 30, 32, 24√2, 26√2, 30√2, 32√2, 46, 48, 36√2, 52, 39√2, 42√2, 46√2.
Code: 525 0 72 394 39 85 266 52 98 467 78 124 466 78 78 136 39 85 265 52 72 65 78 72 362 36 36 424 42 30 240 84 72 183 60 30 487 60 48 160 108 48 60 36 36 320 92 32 321 124 32 300 30 30 301 60 30
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)