Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:126AG2of4 GHM

Order: 20

Horizontal side: 126 Vertical side: 126

Elements: 8√2, 9√2, 14, 16, 18, 14√2, 16√2, 24, 18√2, 28, 20√2, 24√2, 36, 28√2, 42, 48, 54, 56, 70, 63√2.

Code: 707 0 126 423 70 84 567 70 126 636 63 63 280 28 84 281 56 84 142 70 70 141 70 84 90 63 63 162 16 40 161 16 56 82 24 48 204 36 36 180 54 54 181 72 54 545 72 0 246 0 24 485 24 0 361 72 36 245 0 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)