Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:180AF GHM

Order: 18

Horizontal side: 180 Vertical side: 180

Elements: 1√2, 6, 8, 7√2, 8√2, 16, 22, 16√2, 28, 34, 28√2, 56, 68, 56√2, 62√2, 68√2, 112, 90√2.

Code: 1125 0 68 904 90 90 626 118 118 283 118 90 345 118 84 221 112 90 72 119 83 61 118 90 14 119 83 86 112 76 165 120 68 164 136 68 280 152 84 85 112 68 685 0 0 684 68 0 560 124 56 561 180 56

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)