Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:188AH GHM

Order: 18

Horizontal side: 188 Vertical side: 188

Elements: 6√2, 12, 12√2, 18, 18√2, 26, 34, 26√2, 27√2, 42, 33√2, 34√2, 60, 68, 60√2, 94, 128, 94√2.

Code: 1285 0 60 944 94 94 943 188 94 344 128 60 343 162 60 262 188 68 261 188 94 683 188 0 607 0 60 600 60 60 334 93 27 60 126 60 184 144 42 183 162 42 276 93 27 127 120 54 120 132 54 427 120 42

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)