Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:94BC GHM

Order: 18

Horizontal side: 94 Vertical side: 94

Elements: 1√2, 5, 6√2, 7√2, 12, 14, 11√2, 17, 19, 14√2, 22, 28, 22√2, 33, 33√2, 47, 61, 47√2.

Code: 615 0 33 474 47 47 473 94 47 144 61 33 143 75 33 72 82 40 191 94 47 66 76 34 125 82 28 10 76 34 337 0 33 330 33 33 224 55 11 223 77 11 55 77 28 177 77 28 283 94 0 114 66 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)