Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:80AA GHM

Order: 18

Horizontal side: 80 Vertical side: 80

Elements: 2√2, 5√2, 7√2, 14, 16, 18, 14√2, 22, 16√2, 18√2, 26, 20√2, 21√2, 22√2, 36, 26√2, 31√2, 44.

Code: 312 31 49 264 26 54 263 52 54 212 73 59 144 66 66 143 80 66 74 73 59 443 80 22 54 31 49 363 36 18 162 52 38 161 52 54 22 38 20 224 58 0 223 80 0 200 38 20 185 0 0 184 18 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)