Primitive Perfect Isosceles Right Triangled Square

Title: dr 19:144AZ4of4 GHM

Order: 19

Horizontal side: 144 Vertical side: 144

Elements: 2√2, 4, 4√2, 8, 6√2, 11, 8√2, 11√2, 14√2, 22, 28, 33, 44, 50, 61, 72, 83, 61√2, 72√2.

Code: 835 0 61 724 72 72 723 144 72 114 83 61 113 94 61 445 94 28 501 144 72 617 0 61 610 61 61 331 94 61 281 122 28 142 136 14 84 130 20 83 138 20 62 144 22 223 144 0 44 134 16 43 138 16 24 136 14

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)

83
72√2
72
11√2
11
44
50
61
61√2
33
28
14√2
8√2
8
6√2
22
4√2
4
2√2