Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:149AA GHM

Order: 19

Horizontal side: 149 Vertical side: 149

Elements: 4√2, 8, 8√2, 13, 12√2, 16√2, 26, 28, 26√2, 28√2, 40, 41, 54, 40√2, 41√2, 67, 54√2, 82, 95.

Code: 957 0 149 673 95 82 547 95 149 546 95 95 135 95 82 286 0 54 405 28 42 404 68 42 823 108 0 412 149 41 285 0 26 82 36 34 81 36 42 42 40 38 164 52 26 413 149 0 120 40 38 265 0 0 264 26 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)