Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:168AS GHM

Order: 20

Horizontal side: 168 Vertical side: 168

Elements: 6, 5√2, 10, 14, 10√2, 11√2, 14√2, 22, 24, 22√2, 24√2, 48, 38√2, 58, 48√2, 72, 82, 86, 96, 72√2.

Code: 967 0 168 583 96 110 727 96 168 863 168 82 380 38 110 224 60 88 223 82 88 142 96 96 141 96 110 114 71 77 63 82 82 56 71 77 107 76 82 100 86 82 821 168 82 485 0 24 484 48 24 720 96 72 245 0 0 244 24 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)