Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:294AB GHM

Order: 20

Horizontal side: 294 Vertical side: 294

Elements: 8, 11√2, 22, 48, 56, 42√2, 63, 64, 48√2, 84, 85, 64√2, 96, 72√2, 104, 83√2, 84√2, 126, 105√2, 126√2.

Code: 1267 0 294 1266 0 168 1047 126 294 563 230 238 647 230 294 646 230 230 480 174 238 481 222 238 722 294 166 81 230 238 855 126 105 961 222 190 842 84 84 836 211 83 637 126 105 1050 189 105 221 211 105 112 222 94 843 84 0 422 126 42

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)