Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:192BF JDS

Order: 20

Horizontal side: 192 Vertical side: 192

Elements: 1, 1√2, 2, 3, 3√2, 6, 6√2, 12, 12√2, 24, 24√2, 48, 63, 64, 65, 48√2, 64√2, 96, 128, 96√2.

Code: 1285 0 64 964 96 96 963 192 96 244 120 72 243 144 72 487 144 96 486 144 48 64 126 66 63 132 66 127 132 72 126 132 60 21 128 66 12 129 65 11 129 66 37 129 66 36 129 63 653 129 0 645 0 0 644 64 0 635 129 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)