Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:342AL GHM

Order: 20

Horizontal side: 342 Vertical side: 342

Elements: 11, 11√2, 22, 16√2, 20√2, 32, 24√2, 40, 32√2, 48, 46√2, 72, 81, 92, 114, 136, 114√2, 125√2, 228, 171√2.

Code: 2285 0 114 1714 171 171 1256 217 217 466 171 171 815 217 136 117 217 136 116 217 125 227 228 136 1363 250 0 322 282 104 481 298 136 242 322 112 1145 0 0 1144 114 0 403 322 72 202 342 92 323 282 72 162 298 88 923 342 0 727 250 72

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)