Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:192AL GHM

Order: 20

Horizontal side: 192 Vertical side: 192

Elements: 7√2, 9√2, 18, 15√2, 30, 22√2, 29√2, 42, 33√2, 50, 58, 42√2, 63, 66, 50√2, 79, 84, 63√2, 100, 75√2.

Code: 752 75 117 661 66 192 332 99 159 634 129 129 633 192 129 156 84 144 305 99 129 183 84 126 222 106 122 74 106 122 290 113 129 791 192 129 94 75 117 843 84 42 587 84 100 1003 142 0 502 192 50 503 192 0 425 0 0 424 42 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)