Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:295AA GHM

Order: 20

Horizontal side: 295 Vertical side: 295

Elements: 28√2, 38√2, 56, 58, 59, 60, 61, 76, 56√2, 59√2, 60√2, 61√2, 92, 76√2, 117, 84√2, 119, 120, 122, 117√2.

Code: 1197 0 295 606 59 235 1207 119 295 286 211 267 567 239 295 566 239 239 923 211 175 842 295 183 596 0 176 605 59 175 1223 295 61 595 0 117 585 59 117 764 135 99 763 211 99 1177 0 117 1170 117 117 384 173 61 614 234 0 613 295 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)