Primitive Perfect Isosceles Right Triangled Square
Title: __ 19:105AH GHM
Order: 19
Horizontal side: 105 Vertical side: 105
Elements: 5, 7, 10, 12, 15, 17, 18, 15√2, 25, 18√2, 29, 30, 35, 40, 29√2, 47, 35√2, 58, 70.
Code: 705 0 35 581 58 105 292 87 76 471 105 105 293 87 47 182 105 58 183 105 40 121 70 47 177 70 47 73 87 40 103 80 30 257 80 40 403 105 0 355 0 0 354 35 0 53 70 30 303 65 0 152 80 15 151 80 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)