Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:76AI GHM

Order: 20

Horizontal side: 76 Vertical side: 76

Elements: 3√2, 5, 5√2, 8, 6√2, 7√2, 10, 8√2, 12, 14, 15, 12√2, 20, 18√2, 22√2, 34, 36, 40, 42, 34√2.

Code: 425 0 34 361 36 76 182 54 58 401 76 76 126 42 46 222 76 36 66 36 40 125 42 34 153 76 21 347 0 34 340 34 34 201 54 34 70 61 21 101 71 21 52 76 16 51 76 21 86 68 8 141 68 14 32 71 11 85 68 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)