Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:124BZ1of2 GHM

Order: 19

Horizontal side: 124 Vertical side: 124

Elements: 2√2, 3√2, 6, 6√2, 7√2, 9√2, 14, 18, 14√2, 16√2, 30, 32, 30√2, 32√2, 46, 39√2, 46√2, 78, 62√2.

Code: 785 0 46 624 62 62 306 94 94 323 94 62 305 94 64 65 94 58 64 100 58 96 97 55 187 106 64 326 92 32 164 78 46 26 92 60 140 92 60 34 97 55 465 0 0 464 46 0 76 85 39 147 92 46 390 85 39

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)

78
62√2
30√2
32
30
6
6√2
9√2
18
32√2
16√2
2√2
14√2
3√2
46
46√2
7√2
14
39√2