Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:168AB1of2 GHM

Order: 20

Horizontal side: 168 Vertical side: 168

Elements: 3√2, 6, 6√2, 12, 9√2, 17√2, 30, 36, 38, 32√2, 36√2, 38√2, 60, 64, 49√2, 70, 72, 76, 60√2, 66√2.

Code: 707 0 168 380 70 168 381 108 168 602 168 108 601 168 168 326 0 98 645 32 66 761 108 130 723 168 36 492 49 49 174 49 49 660 66 66 301 96 66 92 105 57 30 105 57 60 102 54 61 108 54 127 96 48 364 132 0 363 168 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)