Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:116BB3of4 GHM

Order: 18

Horizontal side: 116 Vertical side: 116

Elements: 1√2, 2, 2√2, 3√2, 6, 6√2, 10, 10√2, 16√2, 26, 32, 26√2, 42, 32√2, 58, 42√2, 74, 58√2.

Code: 745 0 42 584 58 58 583 116 58 164 74 42 260 90 58 261 116 58 427 0 42 420 42 42 104 52 32 16 61 41 27 62 42 26 62 40 107 64 42 30 61 41 60 58 38 61 64 38 324 84 0 323 116 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)