Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:75AC GHM

Order: 20

Horizontal side: 75 Vertical side: 75

Elements: 2√2, 4, 4√2, 6, 8, 6√2, 8√2, 12, 9√2, 16, 12√2, 14√2, 16√2, 24, 27, 32, 24√2, 27√2, 40, 51.

Code: 517 0 75 160 51 75 161 67 75 82 75 67 81 75 75 403 75 27 146 21 45 327 35 59 96 12 36 125 21 33 120 12 36 65 21 27 64 27 27 20 33 33 40 31 31 41 35 31 274 48 0 273 75 0 247 0 24 240 24 24

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)