Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:150AM GHM

Order: 18

Horizontal side: 150 Vertical side: 150

Elements: 2√2, 6√2, 12, 11√2, 12√2, 22, 24, 20√2, 22√2, 35, 40, 29√2, 44, 55, 75, 55√2, 95, 75√2.

Code: 955 0 55 754 75 75 753 150 75 204 95 55 60 115 75 351 150 75 120 109 69 121 121 69 292 150 40 20 97 57 241 121 57 557 0 55 550 55 55 441 99 55 222 121 33 403 150 0 223 121 11 114 110 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)