Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:126AG GHM

Order: 19

Horizontal side: 126 Vertical side: 126

Elements: 1, 1√2, 5, 7, 5√2, 8, 9, 7√2, 14, 13√2, 14√2, 18√2, 36, 36√2, 54, 45√2, 72, 54√2, 63√2.

Code: 725 0 54 634 63 63 456 81 81 130 81 81 50 68 68 51 73 68 77 73 68 76 73 61 147 80 68 140 94 68 91 72 63 17 72 63 16 72 62 85 72 54 545 0 0 544 54 0 180 108 54 360 90 36 361 126 36

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)

72
63√2
45√2
13√2
5√2
5
7
7√2
14
14√2
9
1
1√2
8
54
54√2
18√2
36√2
36