Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:166BE GHM

Order: 19

Horizontal side: 166 Vertical side: 166

Elements: 8, 8√2, 16, 14√2, 16√2, 28, 32, 23√2, 28√2, 42, 46, 50, 37√2, 60, 46√2, 74, 60√2, 92, 106.

Code: 1065 0 60 921 92 166 505 92 116 741 166 166 427 92 116 286 106 88 87 134 116 80 142 116 167 134 108 160 150 108 327 134 92 466 120 46 146 92 74 285 106 60 607 0 60 600 60 60 374 97 23 236 97 23 465 120 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)

106
92
50
74
42
28√2
8
8√2
16
16√2
32
46√2
14√2
28
60
60√2
37√2
23√2
46