Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:192BH3of4 GHM

Order: 20

Horizontal side: 192 Vertical side: 192

Elements: 1√2, 2, 2√2, 4, 3√2, 4√2, 5√2, 9√2, 14, 18, 32, 46, 50, 64, 46√2, 82, 64√2, 96, 128, 96√2.

Code: 1285 0 64 964 96 96 963 192 96 321 128 96 147 128 96 56 137 91 42 146 92 501 192 96 43 146 88 462 192 46 90 137 91 25 142 86 24 144 86 36 143 85 14 143 85 187 128 82 823 146 0 645 0 0 644 64 0 463 192 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)