Primitive Perfect Isosceles Right Triangled Square

Title: _r 18:184AI3of4 GHM

Order: 18

Horizontal side: 184 Vertical side: 184

Elements: 8√2, 10√2, 16, 20, 20√2, 30, 23√2, 40, 30√2, 46, 38√2, 60, 62, 46√2, 76, 69√2, 108, 92√2.

Code: 1087 0 184 403 108 144 202 128 164 301 138 184 462 184 138 461 184 184 203 128 144 102 138 154 623 138 92 306 38 114 607 68 144 696 115 69 380 38 114 86 68 84 167 76 92 920 92 92 234 115 69 767 0 76

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)