Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:178AC1of2 GHM

Order: 18

Horizontal side: 178 Vertical side: 178

Elements: 4, 4√2, 8, 8√2, 16, 16√2, 28, 29, 29√2, 30√2, 31√2, 58, 59, 60, 59√2, 89, 119, 89√2.

Code: 1195 0 59 894 89 89 893 178 89 304 119 59 583 149 31 292 178 60 291 178 89 603 178 0 597 0 59 590 59 59 164 75 43 163 91 43 287 91 59 84 83 35 83 91 35 44 87 31 43 91 31 314 118 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)