Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:71AA GHM

Order: 20

Horizontal side: 71 Vertical side: 71

Elements: 7, 9, 7√2, 9√2, 13, 14, 10√2, 11√2, 18, 13√2, 15√2, 22, 23, 24, 18√2, 26, 22√2, 24√2, 36, 38.

Code: 245 0 47 244 24 47 100 48 71 231 71 71 143 38 47 72 45 54 71 45 61 137 45 61 130 58 61 363 45 18 152 60 33 261 71 48 387 0 47 110 60 33 220 49 22 221 71 22 96 0 9 185 9 0 184 27 0 95 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)