Primitive Perfect Isosceles Right Triangled Square
Title: _d 19:304AH GHM
Order: 19
Horizontal side: 304 Vertical side: 304
Elements: 5√2, 10, 10√2, 20, 28, 20√2, 28√2, 42, 35√2, 56, 42√2, 56√2, 82, 96, 124, 152, 124√2, 180, 152√2.
Code: 1805 0 124 1524 152 152 1523 304 152 284 180 124 283 208 124 352 243 117 961 304 152 1247 0 124 1240 124 124 424 166 82 423 208 82 50 243 117 100 238 112 101 248 112 562 304 56 200 228 102 201 248 102 821 248 82 563 304 0
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)