Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:112AY GHM

Order: 20

Horizontal side: 112 Vertical side: 112

Elements: 1√2, 2, 2√2, 3√2, 14, 10√2, 12√2, 18, 14√2, 20, 24, 28, 20√2, 40, 44, 32√2, 48, 34√2, 68, 56√2.

Code: 685 0 44 564 56 56 326 80 80 243 80 56 185 80 62 32 83 59 24 82 60 23 84 60 147 84 62 140 98 62 14 83 59 403 84 20 124 68 44 287 84 48 483 112 0 445 0 0 344 34 10 106 34 10 205 44 0 204 64 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)