Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:160BX2of2 GHM

Order: 20

Horizontal side: 160 Vertical side: 160

Elements: 2√2, 6, 7√2, 10, 8√2, 14, 10√2, 16, 12√2, 14√2, 20, 22√2, 36, 44, 58, 51√2, 80, 58√2, 102, 80√2.

Code: 1025 0 58 804 80 80 803 160 80 224 102 58 86 116 72 165 124 64 361 160 80 143 116 58 142 130 58 61 130 64 107 130 64 106 130 54 205 140 44 585 0 0 584 58 0 76 109 51 26 128 56 120 128 56 510 109 51 441 160 44

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)