Primitive Perfect Isosceles Right Triangled Square
Title: _d 19:304BA GHM
Order: 19
Horizontal side: 304 Vertical side: 304
Elements: 3√2, 12√2, 18, 15√2, 24, 18√2, 30, 44, 44√2, 64, 66, 88, 64√2, 66√2, 108, 152, 108√2, 196, 152√2.
Code: 1965 0 108 1524 152 152 1523 304 152 444 196 108 443 240 108 642 304 88 641 304 152 1087 0 108 1080 108 108 664 174 42 663 240 42 883 304 0 301 204 42 152 219 27 184 222 24 183 240 24 30 219 27 126 204 12 247 216 24
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)