Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:84AC GHM

Order: 19

Horizontal side: 84 Vertical side: 84

Elements: 2√2, 4, 4√2, 8, 6√2, 9, 8√2, 14, 18, 14√2, 21, 15√2, 18√2, 28, 21√2, 36, 33√2, 36√2, 42√2.

Code: 422 42 42 364 36 48 26 70 82 47 72 84 46 72 80 87 76 84 86 76 76 283 70 54 142 84 68 143 84 54 66 36 48 215 42 33 214 63 33 363 84 18 93 42 33 330 33 33 154 48 18 184 66 0 183 84 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)