Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:150AD GHM

Order: 18

Horizontal side: 150 Vertical side: 150

Elements: 7√2, 11√2, 13√2, 22, 26, 30, 22√2, 24√2, 40, 30√2, 44, 37√2, 40√2, 60, 53√2, 55√2, 80, 60√2.

Code: 602 60 90 534 53 97 226 84 128 447 106 150 556 95 95 246 60 104 225 84 106 265 84 80 114 95 95 76 53 97 372 97 67 603 60 30 134 97 67 803 110 0 402 150 40 403 150 0 305 0 0 304 30 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)