Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:189AD GHM

Order: 20

Horizontal side: 189 Vertical side: 189

Elements: 8√2, 16, 12√2, 16√2, 24, 32, 27√2, 48, 52, 53, 54, 56, 41√2, 52√2, 54√2, 55√2, 56√2, 81, 82, 81√2.

Code: 817 0 189 816 0 108 527 81 189 526 81 137 567 133 189 566 133 133 552 136 82 485 133 85 542 54 54 321 165 85 162 181 69 161 181 85 82 189 77 823 136 0 412 177 41 243 189 53 543 54 0 272 81 27 124 177 41 533 189 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)