Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:256BA GHM

Order: 20

Horizontal side: 256 Vertical side: 256

Elements: 2, 2√2, 5√2, 7√2, 12, 12√2, 24, 36, 36√2, 62, 64, 66, 60√2, 62√2, 64√2, 66√2, 126, 128, 130, 128√2.

Code: 1305 0 126 1284 128 128 1283 256 128 24 130 126 76 125 121 625 132 66 624 194 66 646 192 64 1265 0 0 604 60 66 243 120 102 122 132 114 54 125 121 123 132 102 360 96 102 361 132 102 664 126 0 663 192 0 27 192 66 645 192 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)