Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:241AC3of8 GHM

Order: 20

Horizontal side: 241 Vertical side: 241

Elements: 2√2, 4, 4√2, 8, 6√2, 12, 14, 13√2, 14√2, 27, 20√2, 40, 40√2, 67, 94, 67√2, 87√2, 134, 107√2, 174.

Code: 1747 0 241 1343 174 107 672 241 174 671 241 241 876 154 87 406 0 67 947 40 107 1070 134 107 204 154 87 405 0 27 275 0 0 121 12 27 62 18 21 144 26 13 143 40 13 46 14 17 85 18 13 26 12 15 45 14 13 134 27 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)