Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:242AO GHM

Order: 20

Horizontal side: 242 Vertical side: 242

Elements: 8, 8√2, 16, 12√2, 16√2, 28, 28√2, 31√2, 34√2, 38√2, 56, 62, 46√2, 68, 62√2, 90, 118, 124, 90√2, 121√2.

Code: 1245 0 118 1214 121 121 906 152 152 316 121 121 905 152 62 1185 0 0 464 46 72 86 84 110 165 92 102 164 108 102 280 124 118 386 46 72 85 84 102 685 84 34 124 96 90 561 152 90 287 152 62 620 180 62 621 242 62 344 118 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)