Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:114AY GHM

Order: 19

Horizontal side: 114 Vertical side: 114

Elements: 2, 2√2, 8, 10, 8√2, 9√2, 14, 12√2, 17, 14√2, 24, 31, 33, 24√2, 45, 57, 45√2, 69, 57√2.

Code: 695 0 45 574 57 57 573 114 57 124 69 45 103 81 47 92 90 48 331 114 57 173 90 31 242 114 24 20 71 47 21 73 47 82 81 39 81 81 47 457 0 45 450 45 45 144 59 31 143 73 31 311 90 31 243 114 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)