Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:112AF1of2 GHM

Order: 20

Horizontal side: 112 Vertical side: 112

Elements: 3, 3√2, 6, 6√2, 9, 15, 15√2, 16√2, 27, 20√2, 22√2, 32, 40, 42, 44, 32√2, 48, 52, 40√2, 48√2.

Code: 487 0 112 486 0 64 527 48 112 30 100 112 31 103 112 97 103 112 156 97 97 273 97 82 62 103 103 61 103 109 155 97 82 220 70 82 421 112 82 322 32 32 447 48 60 200 92 60 400 72 40 401 112 40 323 32 0 162 48 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)