Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:196AE GHM

Order: 19

Horizontal side: 196 Vertical side: 196

Elements: 3, 3√2, 6, 9, 9√2, 16, 15√2, 16√2, 18√2, 32, 34, 32√2, 64, 66, 82, 98, 114, 82√2, 98√2.

Code: 1145 0 82 984 98 98 983 196 98 164 114 82 163 130 82 345 130 64 661 196 98 827 0 82 820 82 82 184 100 64 30 118 82 31 121 82 97 121 82 96 121 73 150 115 79 61 121 79 641 164 64 322 196 32 323 196 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)