Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:264AB GHM

Order: 20

Horizontal side: 264 Vertical side: 264

Elements: 6√2, 15√2, 22, 30, 22√2, 30√2, 56, 45√2, 68, 74, 56√2, 82, 86, 92, 104, 74√2, 116, 86√2, 92√2, 104√2.

Code: 1045 0 160 1044 104 160 823 208 182 562 264 208 561 264 264 1163 264 92 220 126 182 221 148 182 452 193 137 304 178 152 303 208 152 745 0 86 744 74 86 683 148 92 154 193 137 60 80 92 924 172 0 923 264 0 867 0 86 860 86 86

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)