Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:273AA GHM

Order: 20

Horizontal side: 273 Vertical side: 273

Elements: 7, 11√2, 34, 31√2, 34√2, 41√2, 60, 62, 71, 82, 60√2, 62√2, 89, 90, 93, 71√2, 120, 90√2, 142, 101√2.

Code: 1012 101 172 904 90 183 903 180 183 622 242 211 931 273 273 623 242 149 312 273 180 114 101 172 410 112 183 344 146 149 343 180 149 1203 273 60 71 153 149 897 153 149 716 0 71 1425 71 0 821 153 142 715 0 0 604 213 0 603 273 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)