Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:176AD GHM

Order: 20

Horizontal side: 176 Vertical side: 176

Elements: 12, 16√2, 26, 32, 23√2, 26√2, 32√2, 46, 48, 35√2, 52, 58, 64, 46√2, 66, 70, 72, 52√2, 54√2, 64√2.

Code: 727 0 176 460 72 176 461 118 176 232 141 153 581 176 176 350 141 153 260 26 130 261 52 130 667 52 130 540 106 118 701 176 118 522 52 52 521 52 104 127 52 64 640 64 64 641 128 64 322 160 32 321 160 64 162 176 48 483 176 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)