Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:138AF GHM

Order: 18

Horizontal side: 138 Vertical side: 138

Elements: 2√2, 6, 5√2, 10, 10√2, 11√2, 12√2, 14√2, 20, 22, 22√2, 44, 47, 58, 69, 80, 58√2, 69√2.

Code: 805 0 58 694 69 69 693 138 69 114 80 58 50 91 69 471 138 69 63 86 58 107 86 64 106 86 54 205 96 44 587 0 58 580 58 58 144 72 44 26 84 56 120 84 56 441 116 44 222 138 22 223 138 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)