Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AB GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 4√2, 9√2, 18, 26, 24√2, 26√2, 48, 52, 58, 44√2, 78, 58√2, 96, 106, 77√2, 82√2, 116, 92√2, 96√2, 106√2.

Code: 1065 0 164 1064 106 164 580 212 270 581 270 270 483 154 164 242 178 188 1161 270 212 920 178 188 822 82 82 774 77 87 96 77 87 185 86 78 444 130 52 960 174 96 961 270 96 40 82 82 783 78 0 267 78 78 260 104 78 527 78 52

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)