Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:172AJ4of4 GHM

Order: 19

Horizontal side: 172 Vertical side: 172

Elements: 6√2, 12, 12√2, 13√2, 21, 24, 18√2, 26, 21√2, 36, 26√2, 42, 47, 52, 52√2, 78, 94, 73√2, 86√2.

Code: 947 0 172 520 94 172 521 146 172 262 172 146 261 172 172 736 99 73 243 42 96 367 42 120 423 78 78 212 99 99 211 99 120 477 99 120 136 86 86 180 18 96 124 30 84 123 42 84 860 86 86 64 36 78 787 0 78

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)