Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:167AB GHM

Order: 20

Horizontal side: 167 Vertical side: 167

Elements: 1, 1√2, 2, 2√2, 3√2, 5, 7, 5√2, 7√2, 19, 19√2, 43, 57, 43√2, 62, 67, 57√2, 62√2, 105, 110.

Code: 1105 0 57 1051 105 167 627 105 167 626 105 105 192 124 86 193 124 67 432 167 43 57 105 67 56 105 62 75 110 60 74 117 60 673 124 0 17 110 60 10 111 60 34 114 57 27 110 59 20 112 59 575 0 0 574 57 0 433 167 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)