Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:188AL GHM

Order: 20

Horizontal side: 188 Vertical side: 188

Elements: 4√2, 8, 13√2, 26, 34, 26√2, 44, 32√2, 46, 33√2, 34√2, 56, 44√2, 66, 68, 56√2, 86, 88, 66√2, 72√2.

Code: 865 0 102 664 66 122 663 132 122 562 188 132 561 188 188 883 188 44 334 99 89 463 132 76 347 0 102 340 34 102 264 60 76 263 86 76 132 99 89 81 68 76 42 72 72 324 100 44 720 72 72 687 0 68 444 144 0 443 188 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)