Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:125AC GHM

Order: 20

Horizontal side: 125 Vertical side: 125

Elements: 7√2, 8√2, 14, 16, 17, 16√2, 17√2, 28, 24√2, 34, 37, 28√2, 40, 48, 51, 37√2, 40√2, 57, 60, 44√2.

Code: 577 0 125 400 57 125 401 97 125 282 125 97 281 125 125 603 125 37 176 0 68 345 17 51 481 65 85 242 89 61 164 81 69 163 97 69 84 89 61 175 0 51 517 0 51 76 44 44 145 51 37 440 44 44 374 88 0 373 125 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)