Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:206AW GHM

Order: 19

Horizontal side: 206 Vertical side: 206

Elements: 8√2, 9√2, 12√2, 18, 24, 18√2, 20√2, 24√2, 36, 28√2, 47, 48, 56, 47√2, 75, 103, 75√2, 131, 103√2.

Code: 1315 0 75 1034 103 103 1033 206 103 284 131 75 206 139 83 472 206 56 471 206 103 80 139 83 757 0 75 750 75 75 481 123 75 242 147 51 241 147 75 122 159 63 363 159 27 563 206 0 184 141 9 183 159 9 94 150 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)

131
103√2
103
28√2
20√2
47√2
47
8√2
75
75√2
48
24√2
24
12√2
36
56
18√2
18
9√2