Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:96AP GHM

Order: 18

Horizontal side: 96 Vertical side: 96

Elements: 2, 2√2, 4, 3√2, 4√2, 8, 11√2, 21, 15√2, 22, 23, 26, 22√2, 37, 48, 37√2, 59, 48√2.

Code: 595 0 37 484 48 48 483 96 48 114 59 37 30 70 48 261 96 48 83 67 37 42 71 41 41 71 45 22 73 43 21 73 45 235 73 22 213 73 22 377 0 37 370 37 37 154 52 22 224 74 0 223 96 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)