Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:340AG GHM

Order: 20

Horizontal side: 340 Vertical side: 340

Elements: 22, 17√2, 22√2, 26√2, 44, 52, 68, 52√2, 78, 68√2, 102, 104, 112, 126, 134, 136, 102√2, 160, 119√2, 136√2.

Code: 1607 0 340 1343 160 206 1127 160 340 680 272 340 681 340 340 443 204 228 1367 204 272 1366 204 136 225 160 206 224 182 206 1263 204 102 266 0 180 527 26 206 526 26 154 1047 78 206 785 0 102 172 221 119 1190 221 119 1025 0 0 1024 102 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)