Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:124BG GHM

Order: 19

Horizontal side: 124 Vertical side: 124

Elements: 2, 2√2, 6√2, 12, 12√2, 18, 14√2, 22, 28, 22√2, 27√2, 28√2, 40, 29√2, 44, 40√2, 42√2, 68, 62√2.

Code: 685 0 56 624 62 62 443 124 80 126 68 68 225 80 58 224 102 58 406 84 40 66 62 62 125 68 56 25 80 56 24 82 56 296 55 29 187 84 58 282 28 28 281 28 56 142 42 42 274 55 29 420 42 42 405 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)