Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:128AE GHM

Order: 20

Horizontal side: 128 Vertical side: 128

Elements: 4, 12√2, 18, 20, 22, 24, 18√2, 22√2, 23√2, 24√2, 36, 27√2, 40, 42, 44, 40√2, 42√2, 62, 44√2, 66.

Code: 445 0 84 444 44 84 663 88 62 407 88 128 406 88 88 225 88 66 422 42 42 224 22 62 47 88 66 276 65 39 187 92 66 180 110 66 201 42 62 625 42 0 234 65 39 367 92 48 246 104 24 423 42 0 126 92 12 245 104 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)