Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:136AB1of2 GHM

Order: 18

Horizontal side: 136 Vertical side: 136

Elements: 8, 8√2, 12, 11√2, 16, 12√2, 22, 16√2, 17√2, 22√2, 24√2, 34, 34√2, 56, 68, 51√2, 57√2, 68√2.

Code: 682 68 68 574 57 79 220 114 136 221 136 136 240 92 114 164 108 98 163 124 98 122 136 102 121 136 114 683 136 34 84 116 90 83 124 90 116 57 79 567 68 90 176 51 51 510 51 51 344 102 0 343 136 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)