Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:340AX GHM

Order: 20

Horizontal side: 340 Vertical side: 340

Elements: 2√2, 4, 4√2, 6, 6√2, 7√2, 12, 14√2, 46, 46√2, 55√2, 78, 92, 69√2, 85√2, 124, 170, 124√2, 216, 170√2.

Code: 2165 0 124 1704 170 170 1703 340 170 464 216 124 463 262 124 787 262 170 856 255 85 1247 0 124 1240 124 124 694 193 55 146 248 110 556 193 55 125 248 98 65 248 92 64 254 92 20 260 98 40 258 96 41 262 96 925 248 0 74 255 85

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)