Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:139AL GHM

Order: 19

Horizontal side: 139 Vertical side: 139

Elements: 4, 12, 11√2, 16, 12√2, 17, 20, 22, 16√2, 24, 17√2, 20√2, 22√2, 39, 39√2, 50√2, 78, 61√2, 100.

Code: 1007 0 139 783 100 61 392 139 100 391 139 139 506 89 50 226 0 39 162 38 45 161 38 61 205 38 41 204 58 41 610 78 61 114 89 50 43 38 41 126 22 29 247 34 41 225 0 17 125 22 17 175 0 0 174 17 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)