Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:71AE GHM

Order: 20

Horizontal side: 71 Vertical side: 71

Elements: 4√2, 7, 8, 9, 7√2, 11, 9√2, 14, 11√2, 18, 13√2, 14√2, 22, 16√2, 18√2, 27, 28, 22√2, 31√2, 44.

Code: 447 0 71 283 44 43 182 62 53 181 62 71 92 71 62 91 71 71 316 40 31 166 0 27 145 16 29 144 30 29 83 44 35 130 36 35 44 40 31 75 16 22 74 23 22 275 0 0 117 16 22 116 16 11 227 27 22 220 49 22

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)