Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:205AI GHM

Order: 20

Horizontal side: 205 Vertical side: 205

Elements: 1√2, 4√2, 6, 5√2, 8, 6√2, 8√2, 11√2, 12√2, 23, 17√2, 34, 34√2, 57, 80, 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 57 807 34 91 910 114 91 174 131 74 345 0 23 235 0 0 124 12 11 40 24 23 54 29 18 66 28 17 80 20 19 81 28 19 12 29 18 65 28 11 114 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)