Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:166AD GHM

Order: 20

Horizontal side: 166 Vertical side: 166

Elements: 6, 6√2, 8√2, 12, 9√2, 18, 18√2, 32, 35, 27√2, 32√2, 48, 51, 64, 48√2, 70, 51√2, 59√2, 64√2, 67√2.

Code: 707 0 166 640 70 166 641 134 166 322 166 134 321 166 166 676 99 67 60 6 102 61 12 102 185 12 84 184 30 84 276 21 75 512 99 51 511 99 102 357 99 102 482 48 48 121 12 96 94 21 75 82 107 59 590 107 59 483 48 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)