Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:156AG GHM

Order: 19

Horizontal side: 156 Vertical side: 156

Elements: 1, 1√2, 2, 2√2, 3√2, 7, 5√2, 10, 22√2, 27√2, 44, 34√2, 39√2, 44√2, 46√2, 68, 78, 88, 78√2.

Code: 885 0 68 784 78 78 783 156 78 101 88 78 75 88 71 344 122 44 396 117 39 17 88 71 10 89 71 34 92 68 270 95 71 27 88 70 20 90 70 685 0 0 464 46 22 226 46 22 447 68 44 440 112 44 54 117 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)