Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:137AA GHM

Order: 18

Horizontal side: 137 Vertical side: 137

Elements: 1√2, 2, 2√2, 3√2, 6, 16, 16√2, 32, 27√2, 41, 30√2, 32√2, 48, 41√2, 64, 48√2, 80, 89.

Code: 897 0 137 320 89 137 321 121 137 162 137 121 161 137 137 803 137 41 306 27 75 647 57 105 270 27 75 487 0 48 480 48 48 61 54 48 32 57 45 26 55 43 16 54 42 25 55 41 414 96 0 413 137 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)