Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:176AR GHM

Order: 20

Horizontal side: 176 Vertical side: 176

Elements: 2√2, 4, 4√2, 5√2, 8, 10, 10√2, 22, 16√2, 17√2, 34, 40, 48, 40√2, 48√2, 80, 88, 64√2, 96, 88√2.

Code: 965 0 80 884 88 88 883 176 88 81 96 88 42 100 84 404 136 48 403 176 48 43 100 80 22 102 82 176 85 65 345 102 48 807 0 80 166 64 64 105 80 70 104 90 70 225 80 48 54 85 65 640 64 64 484 128 0 483 176 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)