Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:114AB GHM

Order: 20

Horizontal side: 114 Vertical side: 114

Elements: 1√2, 2, 2√2, 4, 4√2, 8, 8√2, 14, 16, 14√2, 16√2, 17√2, 28, 24√2, 28√2, 48, 56, 41√2, 50√2, 57√2.

Code: 572 57 57 504 50 64 140 100 114 141 114 114 280 86 100 281 114 100 83 58 64 485 58 24 561 114 72 44 54 60 43 58 60 24 56 58 23 58 58 14 57 57 176 41 41 410 41 41 244 82 0 80 106 24 160 98 16 161 114 16

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)