Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:134BK GHM

Order: 19

Horizontal side: 134 Vertical side: 134

Elements: 1, 2√2, 4, 4√2, 6√2, 12, 10√2, 11√2, 12√2, 22, 23, 22√2, 44, 46, 44√2, 45√2, 46√2, 88, 67√2.

Code: 885 0 46 674 67 67 456 89 89 223 89 67 235 89 66 114 78 56 13 89 66 106 78 56 125 88 54 124 100 54 220 112 66 42 92 50 64 94 48 43 92 46 22 94 48 465 0 0 464 46 0 440 90 44 441 134 44

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)

88
67√2
45√2
22
23
11√2
1
10√2
12
12√2
22√2
4√2
6√2
4
2√2
46
46√2
44√2
44