Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:220CC GHM

Order: 19

Horizontal side: 220 Vertical side: 220

Elements: 2√2, 4, 4√2, 6, 6√2, 12, 9√2, 14√2, 16√2, 32, 39, 39√2, 71, 78, 71√2, 110, 78√2, 142, 110√2.

Code: 1425 0 78 1104 110 110 1103 220 110 321 142 110 142 156 96 394 181 71 393 220 71 123 156 84 92 165 87 160 165 87 20 144 84 64 150 78 63 156 78 47 142 82 40 146 82 785 0 0 784 78 0 710 149 71 711 220 71

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)

142
110√2
110
32
14√2
39√2
39
12
9√2
16√2
2√2
6√2
6
4
4√2
78
78√2
71√2
71