Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:221AA GHM

Order: 19

Horizontal side: 221 Vertical side: 221

Elements: 13√2, 26, 24√2, 26√2, 39, 48, 52, 53, 58, 48√2, 72, 53√2, 77, 78, 58√2, 91, 72√2, 110, 91√2.

Code: 915 0 130 914 91 130 130 182 221 391 221 221 783 169 130 267 169 208 260 195 208 527 169 182 1103 221 72 537 0 130 536 0 77 585 53 72 584 111 72 775 0 0 485 53 24 484 101 24 720 149 72 721 221 72 244 77 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)