Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:146BL GHM

Order: 19

Horizontal side: 146 Vertical side: 146

Elements: 1√2, 2, 2√2, 3√2, 6, 6√2, 16, 16√2, 29, 32, 35, 25√2, 41, 32√2, 57, 73, 57√2, 89, 73√2.

Code: 895 0 57 734 73 73 733 146 73 164 89 57 163 105 57 62 111 67 411 146 73 63 111 61 355 111 32 22 107 59 34 108 58 293 111 32 23 107 57 12 108 58 577 0 57 570 57 57 254 82 32 324 114 0 323 146 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)