Primitive Perfect Isosceles Right Triangled Square

Title: _r 18:118AB4of4 GHM

Order: 18

Horizontal side: 118 Vertical side: 118

Elements: 9√2, 12√2, 18, 16√2, 24, 18√2, 32, 24√2, 34, 25√2, 36, 32√2, 48, 34√2, 50, 36√2, 52, 50√2.

Code: 505 0 68 504 50 68 180 100 118 181 118 118 483 82 52 362 118 64 361 118 100 342 34 34 254 25 43 326 86 32 96 25 43 525 34 0 244 58 28 243 82 28 343 34 0 166 70 16 325 86 0 124 70 16

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)