Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:264AC GHM

Order: 20

Horizontal side: 264 Vertical side: 264

Elements: 16√2, 24, 21√2, 32, 42, 32√2, 48, 38√2, 66, 48√2, 68, 76, 84, 90, 76√2, 112, 84√2, 87√2, 90√2, 108√2.

Code: 1082 108 156 874 87 177 663 174 198 907 174 264 906 174 174 216 87 177 427 108 198 380 150 198 241 174 198 1123 112 48 767 112 160 760 188 160 687 112 84 840 180 84 841 264 84 487 0 48 480 48 48 324 80 16 323 112 16 164 96 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)