Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:217AG GHM

Order: 20

Horizontal side: 217 Vertical side: 217

Elements: 6√2, 8√2, 12, 14, 14√2, 24, 28, 22√2, 35√2, 53, 58, 47√2, 70, 53√2, 77, 82, 70√2, 77√2, 82√2, 140.

Code: 1405 0 77 824 82 135 823 164 135 532 217 164 531 217 217 476 170 117 581 140 135 222 162 113 241 164 135 66 164 111 125 170 105 80 162 113 146 140 91 287 154 105 350 182 105 145 140 77 775 0 0 774 77 0 700 147 70 701 217 70

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)