Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:254AO GHM

Order: 20

Horizontal side: 254 Vertical side: 254

Elements: 20, 24, 21√2, 32, 24√2, 42, 44, 48, 42√2, 64, 48√2, 74, 84, 64√2, 96, 74√2, 106, 84√2, 95√2, 106√2.

Code: 1065 0 148 1064 106 148 420 212 254 421 254 254 963 170 116 842 254 128 841 254 212 742 74 74 741 74 148 327 74 148 646 190 64 212 95 95 484 122 68 483 170 68 950 95 95 244 146 44 243 170 44 203 190 44 645 190 0 441 190 44

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)