Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:132AX GHM

Order: 19

Horizontal side: 132 Vertical side: 132

Elements: 4, 4√2, 8, 8√2, 9√2, 14, 12√2, 18, 14√2, 20, 28, 20√2, 32√2, 50, 54, 41√2, 50√2, 82, 66√2.

Code: 825 0 50 664 66 66 543 132 78 126 66 66 205 78 58 204 98 58 283 118 50 142 132 64 141 132 78 326 100 32 47 78 58 46 78 54 85 82 50 84 90 50 505 0 0 504 50 0 96 91 41 187 100 50 410 91 41

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)