Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:192BD GHM

Order: 20

Horizontal side: 192 Vertical side: 192

Elements: 1, 1√2, 2, 2√2, 4, 7, 7√2, 14, 14√2, 18√2, 36, 39√2, 57, 64, 71, 78, 57√2, 64√2, 128, 96√2.

Code: 1285 0 64 964 96 96 783 192 114 186 96 96 365 114 78 394 153 75 576 135 57 144 128 64 70 142 78 71 149 78 17 149 78 10 150 78 27 149 77 20 151 77 47 149 75 713 135 0 147 135 71 645 0 0 644 64 0 575 135 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)