Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:242AN GHM

Order: 20

Horizontal side: 242 Vertical side: 242

Elements: 12√2, 24, 24√2, 36, 40, 42, 48, 40√2, 57, 42√2, 61, 72, 80, 57√2, 84, 101, 105, 80√2, 122, 101√2.

Code: 1227 0 242 800 122 242 801 202 242 402 242 202 401 242 242 1016 141 101 420 42 162 421 84 162 572 141 105 571 141 162 617 141 162 847 0 120 723 84 48 1053 141 0 1015 141 0 126 0 36 247 12 48 246 12 24 487 36 48 365 0 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)