Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:304AF GHM

Order: 19

Horizontal side: 304 Vertical side: 304

Elements: 11√2, 22, 24, 30, 22√2, 24√2, 36, 30√2, 33√2, 48, 36√2, 48√2, 74, 104, 128, 152, 176, 128√2, 152√2.

Code: 1765 0 128 1524 152 152 1523 304 152 244 176 128 243 200 128 302 230 122 1041 304 152 1287 0 128 1280 128 128 364 164 92 363 200 92 303 230 92 745 230 48 334 197 59 226 208 70 116 197 59 225 208 48 484 256 0 483 304 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)