Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:328AG GHM

Order: 20

Horizontal side: 328 Vertical side: 328

Elements: 6, 6√2, 12, 9√2, 13, 18, 13√2, 26, 26√2, 52, 61√2, 91, 73√2, 82√2, 91√2, 94√2, 146, 164, 182, 164√2.

Code: 1825 0 146 1644 164 164 1643 328 164 181 182 164 125 182 152 734 255 91 826 246 82 65 182 146 64 188 146 610 194 152 1465 0 0 944 94 52 130 133 91 131 146 91 917 146 91 910 237 91 94 246 82 260 120 78 261 146 78 521 146 52

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)