Primitive Perfect Isosceles Right Triangled Square

Title: _ir 17:35AA6of14 GHM

Order: 17

Horizontal side: 35 Vertical side: 35

Elements: 2, 2√2, 4, 5, 4√2, 6, 7, 5√2, 7√2, 10, 13, 14, 10√2, 15, 14√2, 20, 15√2.

Code: 205 0 15 144 14 21 143 28 21 72 35 28 71 35 35 133 35 15 61 20 21 45 20 17 44 24 17 25 20 15 24 22 15 157 0 15 150 15 15 104 25 5 103 35 5 54 30 0 53 35 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)