Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:140AJ GHM

Order: 19

Horizontal side: 140 Vertical side: 140

Elements: 1√2, 2, 2√2, 4, 6, 7√2, 14, 14√2, 20, 28, 20√2, 28√2, 40, 40√2, 42√2, 64, 56√2, 80, 70√2.

Code: 805 0 60 704 70 70 566 84 84 143 84 70 422 126 42 74 77 63 63 84 64 16 77 63 27 78 64 26 78 62 47 80 64 643 84 0 405 0 20 404 40 20 140 126 42 280 112 28 281 140 28 205 0 0 204 20 0

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)