Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AO GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 11√2, 13√2, 22, 26, 28, 22√2, 33√2, 52, 54, 40√2, 66, 52√2, 54√2, 82, 96, 108, 82√2, 122, 108√2, 135√2.

Code: 1352 135 135 1221 122 270 967 122 270 520 218 270 521 270 270 116 155 207 227 166 218 226 166 196 827 188 218 826 188 136 330 155 207 265 122 148 661 188 174 134 135 135 400 148 148 285 188 108 1080 108 108 1081 216 108 542 270 54 543 270 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)