Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:123AA GHM

Order: 19

Horizontal side: 123 Vertical side: 123

Elements: 1√2, 11√2, 17, 22, 16√2, 30, 31, 22√2, 32, 33, 30√2, 31√2, 44, 45, 47, 49, 60, 62, 45√2.

Code: 455 0 78 454 45 78 443 90 79 222 112 101 331 123 123 223 112 79 112 123 90 603 123 30 10 46 79 171 63 79 497 63 79 477 0 78 160 47 78 316 0 31 625 31 0 321 63 62 315 0 0 304 93 0 303 123 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)