Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:120BC GHM

Order: 19

Horizontal side: 120 Vertical side: 120

Elements: 1√2, 2, 4, 6, 7√2, 10, 12√2, 24, 17√2, 21√2, 24√2, 34, 38, 40, 42, 48, 40√2, 80, 60√2.

Code: 805 0 40 604 60 60 483 120 72 126 60 60 245 72 48 244 96 48 343 120 38 74 79 41 63 86 42 107 86 48 16 79 41 27 80 42 423 82 0 212 103 21 41 86 42 405 0 0 404 40 0 174 103 21 383 120 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)

80
60√2
48
12√2
24
24√2
34
7√2
6
10
1√2
2
42
21√2
4
40
40√2
17√2
38