Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:105AB GHM

Order: 19

Horizontal side: 105 Vertical side: 105

Elements: 1, 1√2, 2, 13√2, 21, 16√2, 28, 21√2, 30, 31, 32, 33, 35, 28√2, 29√2, 42, 47, 56, 42√2.

Code: 477 0 105 313 47 74 307 47 105 280 77 105 281 105 105 23 49 75 355 49 42 561 105 77 15 47 74 14 48 74 333 49 42 166 0 58 327 16 74 292 29 29 134 29 29 420 42 42 421 84 42 212 105 21 213 105 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)