Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:132AW GHM

Order: 19

Horizontal side: 132 Vertical side: 132

Elements: 2, 8, 8√2, 12, 16, 13√2, 16√2, 26, 30, 36, 26√2, 30√2, 48, 36√2, 54, 39√2, 48√2, 54√2, 78.

Code: 785 0 54 484 48 84 483 96 84 367 96 132 366 96 96 125 96 84 304 78 54 303 108 54 162 124 68 163 124 52 82 132 60 83 132 52 545 0 0 544 54 0 23 108 52 136 93 39 267 106 52 266 106 26 390 93 39

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)