Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:113AA GHM

Order: 20

Horizontal side: 113 Vertical side: 113

Elements: 1√2, 2, 2√2, 3√2, 4√2, 6, 8, 8√2, 16, 20√2, 23√2, 33, 24√2, 26√2, 40, 33√2, 56, 40√2, 64, 73.

Code: 737 0 113 240 73 113 204 93 93 163 113 97 46 93 93 85 97 89 84 105 89 643 113 33 266 23 63 567 49 89 230 23 63 407 0 40 400 40 40 61 46 40 32 49 37 26 47 35 16 46 34 25 47 33 334 80 0 333 113 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)