Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:250AK2of2 GHM

Order: 19

Horizontal side: 250 Vertical side: 250

Elements: 16, 16√2, 24, 28, 32, 24√2, 28√2, 40, 32√2, 46, 37√2, 56, 46√2, 74, 102, 74√2, 102√2, 111√2, 176.

Code: 1767 0 250 376 139 213 747 176 250 746 176 176 1110 139 213 286 0 74 567 28 102 240 84 102 241 108 102 407 108 102 1020 148 102 1021 250 102 320 60 78 321 92 78 162 108 62 161 108 78 285 0 46 465 0 0 464 46 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)

176
37√2
74
74√2
111√2
28√2
56
24√2
24
40
102√2
102
32√2
32
16√2
16
28
46
46√2