Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:132AQ GHM

Order: 19

Horizontal side: 132 Vertical side: 132

Elements: 2, 2√2, 5, 7, 6√2, 12, 12√2, 18√2, 31, 33, 36, 30√2, 32√2, 33√2, 35√2, 64, 66, 68, 66√2.

Code: 687 0 132 363 68 96 182 86 114 311 99 132 337 99 132 336 99 99 60 86 114 120 80 108 121 92 108 75 92 101 57 92 101 350 97 101 21 99 101 320 32 96 304 62 66 24 64 64 660 66 66 661 132 66 647 0 64

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)