Primitive Perfect Isosceles Right Triangled Square
Title: __ 19:172AI2of4 GHM
Order: 19
Horizontal side: 172 Vertical side: 172
Elements: 6√2, 12, 12√2, 13√2, 24, 18√2, 26, 21√2, 36, 26√2, 42, 34√2, 52, 60, 52√2, 78, 86, 94, 86√2.
Code: 947 0 172 520 94 172 521 146 172 262 172 146 261 172 172 603 172 86 66 36 114 127 42 120 126 42 108 247 54 120 423 78 78 212 99 99 344 112 86 363 36 78 182 54 96 130 99 99 860 86 86 861 172 86 787 0 78
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)