Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:112AJ GHM

Order: 20

Horizontal side: 112 Vertical side: 112

Elements: 4√2, 8, 14, 11√2, 16, 13√2, 14√2, 22, 16√2, 17√2, 26, 19√2, 28, 32, 34, 28√2, 32√2, 56, 48√2, 56√2.

Code: 565 0 56 564 56 56 486 64 64 196 45 45 322 96 32 282 28 28 341 34 56 172 51 39 114 45 45 130 51 39 323 96 0 162 112 16 283 28 0 142 42 14 40 38 26 261 64 26 81 42 22 225 42 0 163 112 0 143 42 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)