Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:140AC GHM

Order: 19

Horizontal side: 140 Vertical side: 140

Elements: 10, 14√2, 16√2, 25, 28, 21√2, 31, 32, 35, 36, 28√2, 41, 42, 31√2, 36√2, 56, 42√2, 52√2, 70√2.

Code: 702 70 70 561 56 140 282 84 112 424 98 98 423 140 98 283 84 84 355 84 77 214 119 77 316 109 67 144 70 70 323 84 52 257 84 77 413 109 36 107 109 77 315 109 36 520 52 52 164 68 36 364 104 0 363 140 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)