Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:176AK GHM

Order: 20

Horizontal side: 176 Vertical side: 176

Elements: 5√2, 10, 8√2, 10√2, 15√2, 30, 25√2, 40, 46, 50, 56, 40√2, 64, 46√2, 66, 55√2, 56√2, 80, 82, 64√2.

Code: 805 0 96 554 55 121 303 110 146 152 125 161 661 176 176 50 125 161 100 120 156 101 130 156 462 176 110 256 55 121 507 80 146 823 130 64 463 176 64 405 0 56 404 40 56 80 48 64 644 112 0 643 176 0 567 0 56 560 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)