Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:168AQ1of2 GHM

Order: 20

Horizontal side: 168 Vertical side: 168

Elements: 7√2, 14, 10√2, 12√2, 14√2, 20, 24, 20√2, 21√2, 24√2, 40, 42, 30√2, 48, 42√2, 48√2, 74, 84, 96, 84√2.

Code: 965 0 72 844 84 84 843 168 84 124 96 72 100 108 84 304 138 54 426 126 42 743 98 0 207 98 74 200 118 74 485 0 24 484 48 24 407 98 54 216 105 21 425 126 0 245 0 0 244 24 0 70 105 21 147 98 14 140 112 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)