Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:96AZ GHM

Order: 19

Horizontal side: 96 Vertical side: 96

Elements: 1√2, 2, 2√2, 6, 6√2, 12, 14, 18, 22, 24, 18√2, 21√2, 32, 24√2, 26√2, 46, 48, 50, 48√2.

Code: 507 0 96 323 50 64 467 50 96 486 48 48 180 18 64 181 36 64 125 36 52 141 50 64 65 36 46 64 42 46 266 22 26 22 50 50 485 48 0 225 0 24 214 21 25 16 21 25 25 22 24 247 0 24 240 24 24

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)