Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:146BH GHM

Order: 19

Horizontal side: 146 Vertical side: 146

Elements: 4√2, 6√2, 7√2, 12, 11√2, 12√2, 15√2, 22, 24, 19√2, 30, 24√2, 30√2, 43, 58, 73, 58√2, 88, 73√2.

Code: 885 0 58 734 73 73 733 146 73 154 88 58 190 103 73 431 146 73 587 0 58 580 58 58 221 80 58 112 91 47 44 84 54 74 91 47 126 86 42 247 98 54 240 122 54 66 80 36 125 86 30 304 116 0 303 146 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)