Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:342AG GHM

Order: 20

Horizontal side: 342 Vertical side: 342

Elements: 1√2, 24√2, 30√2, 48, 34√2, 35√2, 36√2, 60, 48√2, 68, 70, 72, 68√2, 108, 136, 137, 138, 137√2, 204, 205.

Code: 2055 0 137 2041 204 342 1085 204 234 1381 342 342 482 252 186 481 252 234 242 276 210 601 312 234 302 342 204 723 276 138 362 312 174 1363 342 68 14 205 137 356 171 103 707 206 138 1377 0 137 1370 137 137 344 171 103 684 274 0 683 342 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)