Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:135AA1of2 GHM

Order: 18

Horizontal side: 135 Vertical side: 135

Elements: 5, 5√2, 10, 10√2, 15, 17√2, 32, 33, 34, 35, 33√2, 34√2, 35√2, 50, 67, 68, 50√2, 85.

Code: 855 0 50 681 68 135 342 102 101 671 135 135 343 102 67 332 135 68 333 135 35 174 85 50 323 102 35 507 0 50 500 50 50 104 60 40 103 70 40 157 70 50 54 65 35 53 70 35 354 100 0 353 135 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)