Primitive Perfect Isosceles Right Triangled Square

Title: ___ 17:104AG GHM

Order: 17

Horizontal side: 104 Vertical side: 104

Elements: 7√2, 14, 11√2, 14√2, 20, 22, 20√2, 30, 32, 40, 29√2, 42, 30√2, 44, 32√2, 37√2, 42√2.

Code: 445 0 60 374 37 67 300 74 104 301 104 104 76 37 67 145 44 60 144 58 60 320 72 74 321 104 74 405 0 20 294 29 31 116 29 31 227 40 42 420 62 42 421 104 42 205 0 0 204 20 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)