Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:136AI JDS

Order: 20

Horizontal side: 136 Vertical side: 136

Elements: 2√2, 8, 8√2, 11√2, 16, 14√2, 22, 16√2, 26, 28, 22√2, 24√2, 33√2, 52, 56, 40√2, 42√2, 70, 52√2, 56√2.

Code: 705 0 66 564 56 80 563 112 80 87 112 136 86 112 128 167 120 136 166 120 120 242 136 104 526 84 52 144 70 66 406 44 40 287 84 80 332 33 33 224 22 44 223 44 44 267 44 66 525 84 0 114 33 33 26 42 42 420 42 42

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)