Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:204AG GHM

Order: 20

Horizontal side: 204 Vertical side: 204

Elements: 9√2, 10√2, 18, 13√2, 20, 26, 26√2, 28√2, 48, 34√2, 39√2, 56, 44√2, 48√2, 52√2, 78, 65√2, 74√2, 78√2, 126.

Code: 1267 0 204 746 52 130 787 126 204 786 126 126 526 0 78 652 117 65 442 170 82 340 170 82 392 39 39 90 117 65 563 108 0 282 136 28 181 126 56 106 126 38 207 136 48 480 156 48 481 204 48 130 39 39 260 26 26 261 52 26

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)