Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:304AK GHM

Order: 19

Horizontal side: 304 Vertical side: 304

Elements: 11√2, 22, 30, 22√2, 32, 34, 30√2, 44, 32√2, 60, 44√2, 45√2, 60√2, 92, 122, 152, 122√2, 182, 152√2.

Code: 1825 0 122 1524 152 152 1523 304 152 304 182 122 303 212 122 322 244 120 921 304 152 1227 0 122 1220 122 122 454 167 77 343 212 88 323 244 88 602 304 60 116 167 77 227 178 88 226 178 66 447 200 88 446 200 44 603 304 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)