Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:140AG GHM

Order: 19

Horizontal side: 140 Vertical side: 140

Elements: 4, 3√2, 6, 6√2, 9√2, 18, 22, 18√2, 26, 22√2, 26√2, 30√2, 44, 48, 44√2, 66, 70, 74, 70√2.

Code: 747 0 140 440 74 140 441 118 140 222 140 118 221 140 140 483 140 70 300 30 96 184 48 78 183 66 78 265 66 70 264 92 70 94 57 69 66 60 72 36 57 69 65 60 66 47 66 70 700 70 70 701 140 70 667 0 66

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)