Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:139AB GHM

Order: 19

Horizontal side: 139 Vertical side: 139

Elements: 3√2, 16, 13√2, 22, 16√2, 18√2, 26, 23√2, 36, 38, 46, 47, 36√2, 38√2, 56, 46√2, 47√2, 67, 54√2.

Code: 677 0 139 540 67 139 364 103 103 363 139 103 184 121 85 563 139 47 130 13 85 164 29 69 163 45 69 385 45 47 384 83 47 267 0 72 30 26 72 230 23 69 221 45 69 474 92 0 473 139 0 467 0 46 460 46 46

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)