Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:208AN GHM

Order: 19

Horizontal side: 208 Vertical side: 208

Elements: 12, 15, 12√2, 14√2, 24, 27, 28, 21√2, 24√2, 28√2, 42, 48, 56, 62, 83, 104, 83√2, 125, 104√2.

Code: 1255 0 83 1044 104 104 1043 208 104 214 125 83 246 122 80 485 146 56 621 208 104 837 0 83 830 83 83 271 110 83 157 110 83 126 110 68 245 122 56 125 110 56 561 166 56 282 194 28 281 194 56 142 208 42 423 208 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)