Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:176AN GHM

Order: 20

Horizontal side: 176 Vertical side: 176

Elements: 8√2, 9√2, 11√2, 18, 22, 18√2, 32, 38, 27√2, 48, 38√2, 54, 58, 64, 48√2, 74, 56√2, 80, 64√2, 69√2.

Code: 805 0 96 694 69 107 583 138 118 382 176 138 381 176 176 743 176 64 116 69 107 227 80 118 543 102 64 272 129 91 184 120 100 183 138 100 94 129 91 482 48 48 481 48 96 327 48 96 82 56 56 644 112 0 643 176 0 560 56 56

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)