Primitive Perfect Isosceles Right Triangled Square

Title: e 20:391AA GHM

Order: 20

Horizontal side: 391 Vertical side: 391

Elements: 25√2, 32√2, 50, 64, 49√2, 50√2, 73, 64√2, 94, 96, 98, 73√2, 124, 126, 94√2, 96√2, 171, 124√2, 220, 171√2.

Code: 2207 0 391 1710 220 391 1711 391 391 490 49 220 1244 173 96 1243 297 96 942 391 126 941 391 220 987 0 171 250 98 171 736 0 73 507 73 146 500 123 146 1263 391 0 967 73 96 960 169 96 644 233 32 643 297 32 735 0 0 324 265 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)