Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:80AH GHM

Order: 18

Horizontal side: 80 Vertical side: 80

Elements: 5√2, 8, 6√2, 10, 8√2, 12, 10√2, 16, 12√2, 15√2, 16√2, 25, 30, 32, 35, 25√2, 34√2, 40√2.

Code: 402 40 40 344 34 46 120 68 80 121 80 80 160 56 68 161 72 68 82 80 60 81 80 68 353 80 25 66 34 46 327 40 52 106 30 30 303 30 0 152 45 15 56 40 20 107 45 25 250 55 25 251 80 25

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)