Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:218AG GHM

Order: 20

Horizontal side: 218 Vertical side: 218

Elements: 1, 1√2, 2, 2√2, 4, 11√2, 15√2, 22, 18√2, 29, 36, 29√2, 51, 58, 80, 69√2, 109, 80√2, 138, 109√2.

Code: 1385 0 80 1094 109 109 1093 218 109 294 138 80 293 167 80 152 182 94 511 218 109 186 164 76 365 182 58 805 0 0 804 80 0 116 149 69 225 160 58 41 164 80 22 166 78 21 166 80 12 167 79 11 167 80 690 149 69 581 218 58

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)