Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:205AH GHM

Order: 20

Horizontal side: 205 Vertical side: 205

Elements: 2√2, 4, 4√2, 6√2, 8√2, 20, 23, 17√2, 20√2, 23√2, 34, 40, 34√2, 40√2, 57, 57√2, 74√2, 114, 91√2, 148.

Code: 1487 0 205 1143 148 91 572 205 148 571 205 205 746 131 74 346 0 57 405 34 51 404 74 51 910 114 91 174 131 74 345 0 23 205 34 31 204 54 31 42 38 27 41 38 31 22 40 29 84 46 23 60 40 29 235 0 0 234 23 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)