Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:216AI GHM

Order: 20

Horizontal side: 216 Vertical side: 216

Elements: 6√2, 10, 12, 10√2, 22, 21√2, 42, 31√2, 44, 48, 36√2, 42√2, 60, 44√2, 72, 60√2, 88, 108, 86√2, 108√2.

Code: 1085 0 108 1084 108 108 866 130 130 223 130 108 425 130 88 605 0 48 604 60 48 723 120 36 107 120 108 106 120 98 312 151 67 214 151 67 883 172 0 442 216 44 487 0 48 66 42 42 127 48 48 443 216 0 420 42 42 364 84 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)