Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:340AF GHM

Order: 20

Horizontal side: 340 Vertical side: 340

Elements: 17√2, 26√2, 44, 52, 56, 68, 52√2, 78, 56√2, 68√2, 100, 102, 104, 112, 126, 136, 102√2, 160, 119√2, 136√2.

Code: 1607 0 340 1043 160 236 522 212 288 781 238 340 1022 340 238 1021 340 340 523 212 236 262 238 262 1263 238 136 1196 221 119 560 56 236 561 112 236 1007 112 236 1127 0 180 443 112 136 686 0 68 1367 68 136 1360 204 136 174 221 119 685 0 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)