Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:168AT GHM

Order: 20

Horizontal side: 168 Vertical side: 168

Elements: 2√2, 6, 5√2, 10, 10√2, 11√2, 16, 14√2, 22, 24, 22√2, 24√2, 48, 36√2, 60, 48√2, 72, 96, 72√2, 84√2.

Code: 967 0 168 603 96 108 482 144 120 481 144 168 242 168 144 241 168 168 726 96 72 360 36 108 224 58 86 223 80 86 112 91 97 161 96 108 50 91 97 63 86 86 107 86 92 106 86 82 144 72 72 26 84 84 840 84 84 727 0 72

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)