Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:218AI GHM

Order: 20

Horizontal side: 218 Vertical side: 218

Elements: 2, 7√2, 14, 10√2, 13√2, 14√2, 26, 20√2, 21√2, 42, 44, 46, 33√2, 42√2, 66, 66√2, 76√2, 86√2, 132, 152.

Code: 1527 0 218 1323 152 86 662 218 152 661 218 218 766 142 76 206 0 66 145 20 72 144 34 72 216 27 65 425 48 44 424 90 44 860 132 86 104 142 76 265 20 46 74 27 65 332 33 33 134 33 33 463 46 0 25 46 44 447 46 44

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)