Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:80AO GHM

Order: 18

Horizontal side: 80 Vertical side: 80

Elements: 2, 4√2, 8, 8√2, 12, 9√2, 14, 18, 14√2, 17√2, 18√2, 26, 19√2, 28, 26√2, 27√2, 44, 40√2.

Code: 445 0 36 404 40 40 283 80 52 86 44 44 145 52 38 144 66 38 266 54 26 46 40 40 85 44 36 27 52 38 196 35 19 127 54 38 182 18 18 181 18 36 92 27 27 174 35 19 270 27 27 265 54 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)