Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:100AW GHM

Order: 20

Horizontal side: 100 Vertical side: 100

Elements: 4√2, 8, 6√2, 8√2, 12, 10√2, 12√2, 13√2, 14√2, 20, 16√2, 24, 26, 32, 36, 29√2, 42, 32√2, 58, 50√2.

Code: 585 0 42 504 50 50 363 100 64 146 50 50 127 64 64 126 64 52 247 76 64 326 68 32 82 72 44 83 72 36 42 76 40 425 0 0 294 29 13 60 58 42 106 42 26 207 52 36 166 52 16 325 68 0 136 29 13 265 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)