Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:364AI GHM

Order: 20

Horizontal side: 364 Vertical side: 364

Elements: 6, 6√2, 12, 18, 16√2, 18√2, 32, 36, 34√2, 64, 52√2, 64√2, 67√2, 128, 134, 99√2, 166, 198, 150√2, 182√2.

Code: 1985 0 166 1824 182 182 1506 214 214 323 214 182 342 248 180 164 198 166 363 214 146 520 248 180 1665 0 0 994 99 67 123 178 134 185 178 128 184 196 128 676 99 67 1345 166 0 64 172 128 63 178 128 1281 300 128 642 364 64 643 364 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)