Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:156AA GHM

Order: 19

Horizontal side: 156 Vertical side: 156

Elements: 3√2, 8, 8√2, 16, 20, 24, 20√2, 24√2, 34, 40, 48, 34√2, 54, 48√2, 68, 51√2, 74, 54√2, 68√2.

Code: 685 0 88 684 68 88 200 136 156 201 156 156 86 108 128 165 116 120 401 156 136 743 108 54 85 108 120 247 108 120 240 132 120 487 108 96 486 108 48 345 0 54 344 34 54 545 0 0 544 54 0 36 105 51 510 105 51

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)