Primitive Perfect Isosceles Right Triangled Square

Title: _r 19:150DN3of4 GHM

Order: 19

Horizontal side: 150 Vertical side: 150

Elements: 3√2, 4√2, 6, 8, 8√2, 16, 12√2, 16√2, 19√2, 31, 22√2, 28√2, 44, 50, 56, 50√2, 75, 100, 75√2.

Code: 1005 0 50 754 75 75 753 150 75 224 97 53 190 119 75 311 150 75 36 97 53 67 100 56 563 106 0 282 134 28 164 122 40 163 138 40 82 146 48 505 0 0 504 50 0 83 146 40 42 150 44 443 150 0 124 134 28

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)

100
75√2
75
22√2
19√2
31
3√2
6
56
28√2
16√2
16
8√2
50
50√2
8
4√2
44
12√2