Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:132AZ1of8 GHM

Order: 19

Horizontal side: 132 Vertical side: 132

Elements: 3√2, 4√2, 6, 8, 6√2, 8√2, 12, 16, 12√2, 14√2, 24, 28, 46, 52, 40√2, 43√2, 46√2, 86, 66√2.

Code: 865 0 46 664 66 66 523 132 80 146 66 66 287 80 80 40 108 80 124 120 68 406 92 40 243 104 52 87 104 76 80 112 76 167 104 68 64 86 46 63 92 46 127 92 52 465 0 0 464 46 0 36 89 43 430 89 43

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)