Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:178AB GHM

Order: 18

Horizontal side: 178 Vertical side: 178

Elements: 10√2, 11√2, 20, 22, 16√2, 20√2, 32, 38, 27√2, 40, 54, 46√2, 70, 54√2, 86, 92, 70√2, 108.

Code: 1085 0 70 921 92 178 462 138 132 861 178 178 206 118 112 405 138 92 106 108 102 205 118 92 166 92 86 325 108 70 221 140 92 112 151 81 381 178 92 270 151 81 705 0 0 704 70 0 540 124 54 541 178 54

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)