Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:76AH GHM

Order: 20

Horizontal side: 76 Vertical side: 76

Elements: 3√2, 5, 4√2, 5√2, 8, 6√2, 7√2, 10, 8√2, 12, 14, 15, 12√2, 20, 18√2, 22√2, 36, 40, 34√2, 38√2.

Code: 407 0 76 220 40 76 151 55 76 57 55 76 50 60 76 84 68 68 83 76 68 107 55 71 30 65 71 76 55 61 147 62 68 346 42 34 180 18 54 124 30 42 123 42 42 207 42 54 64 36 36 46 38 38 380 38 38 367 0 36

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)