Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:192BG GHM

Order: 20

Horizontal side: 192 Vertical side: 192

Elements: 1√2, 2, 2√2, 4, 6, 5√2, 8, 10, 12√2, 24, 24√2, 48, 62, 64, 66, 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 81 128 72 67 128 72 56 129 67 107 134 72 126 132 60 10 129 67 27 128 66 663 130 0 45 130 62 645 0 0 644 64 0 625 130 0 24 132 60

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)