Primitive Perfect Isosceles Right Triangled Square

Title: e 20:341AG GHM

Order: 20

Horizontal side: 341 Vertical side: 341

Elements: 21√2, 28√2, 42, 56, 42√2, 43√2, 63, 56√2, 82, 84, 86, 65√2, 108, 110, 82√2, 84√2, 149, 108√2, 192, 149√2.

Code: 1927 0 341 1490 192 341 1491 341 341 430 43 192 1084 151 84 1083 259 84 822 341 110 821 341 192 867 0 149 650 86 149 1103 341 0 216 0 63 427 21 84 426 21 42 847 63 84 840 147 84 564 203 28 563 259 28 635 0 0 284 231 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)