Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:264AO GHM

Order: 20

Horizontal side: 264 Vertical side: 264

Elements: 5√2, 10, 20, 16√2, 32, 32√2, 33√2, 56, 43√2, 64, 66, 76, 89, 66√2, 96, 99, 76√2, 112, 132, 132√2.

Code: 1325 0 132 1324 132 132 766 188 188 563 188 132 765 188 112 662 66 66 991 99 132 897 99 132 203 188 112 643 168 48 967 168 112 1123 264 0 663 66 0 332 99 33 50 104 48 324 136 16 323 168 16 107 99 43 430 109 43 164 152 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)