Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:170BB GHM

Order: 19

Horizontal side: 170 Vertical side: 170

Elements: 6√2, 10, 12, 9√2, 10√2, 12√2, 18, 20, 24, 20√2, 24√2, 34, 50, 70, 50√2, 76, 70√2, 100, 85√2.

Code: 1005 0 70 854 85 85 763 170 94 96 85 85 187 94 94 126 100 82 247 112 94 240 136 94 341 170 94 66 94 76 125 100 70 705 0 0 704 70 0 200 140 70 201 160 70 102 170 60 103 170 50 500 120 50 501 170 50

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
85√2
76
9√2
18
12√2
24
24√2
34
6√2
12
70
70√2
20√2
20
10√2
10
50√2
50