Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:254AJ GHM

Order: 20

Horizontal side: 254 Vertical side: 254

Elements: 9, 24, 33, 24√2, 42, 32√2, 48, 53, 42√2, 64, 48√2, 53√2, 84, 64√2, 95, 96, 106, 84√2, 95√2, 106√2.

Code: 1065 0 148 1064 106 148 420 212 254 421 254 254 840 170 212 841 254 212 535 0 95 534 53 95 333 86 95 247 86 128 246 86 104 487 110 128 486 110 80 967 158 128 646 190 64 95 86 95 957 0 95 950 95 95 326 158 32 645 190 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)