Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:460AG GHM

Order: 20

Horizontal side: 460 Vertical side: 460

Elements: 22, 22√2, 34, 36, 34√2, 36√2, 58, 68, 72, 64√2, 94, 68√2, 83√2, 136, 158, 166, 147√2, 158√2, 302, 230√2.

Code: 3025 0 158 2304 230 230 1476 313 313 830 313 313 721 302 230 362 338 194 941 396 230 642 460 166 363 338 158 585 338 136 1663 460 0 1585 0 0 1584 158 0 220 316 158 221 338 158 1363 294 0 682 362 68 681 362 136 342 396 102 341 396 136

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)