Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:170BG5of8 GHM

Order: 19

Horizontal side: 170 Vertical side: 170

Elements: 1√2, 2, 2√2, 4, 5√2, 6√2, 10, 14, 16√2, 23√2, 39, 46, 39√2, 62, 46√2, 85, 62√2, 108, 85√2.

Code: 1085 0 62 854 85 85 853 170 85 234 108 62 390 131 85 391 170 85 627 0 62 620 62 62 164 78 46 20 94 62 21 96 62 12 97 61 64 102 56 50 97 61 143 92 46 47 92 60 107 92 56 464 124 0 463 170 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)

108
85√2
85
23√2
39√2
39
62
62√2
16√2
2√2
2
1√2
6√2
5√2
14
4
10
46√2
46