Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:146AE GHM

Order: 19

Horizontal side: 146 Vertical side: 146

Elements: 2√2, 4, 4√2, 8, 9, 9√2, 10√2, 18, 14√2, 20, 20√2, 31, 40, 53, 63, 73, 83, 63√2, 73√2.

Code: 835 0 63 734 73 73 733 146 73 104 83 63 20 93 73 531 146 73 83 91 63 42 95 67 41 95 71 315 95 40 183 95 49 637 0 63 630 63 63 144 77 49 94 86 40 93 95 40 401 126 40 202 146 20 203 146 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)