Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:71AC GHM

Order: 20

Horizontal side: 71 Vertical side: 71

Elements: 2√2, 4, 7, 9, 7√2, 9√2, 13, 14, 10√2, 17, 18, 13√2, 23, 18√2, 26, 31, 22√2, 24√2, 36, 31√2.

Code: 315 0 40 314 31 40 90 62 71 91 71 71 363 53 26 182 71 44 181 71 62 226 49 22 177 0 40 76 10 33 147 17 40 106 0 23 75 10 26 137 10 26 136 10 13 267 23 26 26 47 24 47 49 26 240 47 24 235 0 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)