Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:104BB GHM

Order: 18

Horizontal side: 104 Vertical side: 104

Elements: 1√2, 2, 2√2, 8√2, 13, 15, 11√2, 16, 13√2, 22, 28, 30, 22√2, 41, 52, 41√2, 63, 52√2.

Code: 635 0 41 524 52 52 523 104 52 114 63 41 80 74 52 301 104 52 10 66 44 161 82 44 222 104 22 20 65 43 21 67 43 155 67 28 417 0 41 410 41 41 134 54 28 133 67 28 281 82 28 223 104 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)