Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:196AJ1of2 GHM

Order: 19

Horizontal side: 196 Vertical side: 196

Elements: 2√2, 4, 3√2, 4√2, 6, 6√2, 14, 18, 17√2, 26√2, 46, 52, 46√2, 72, 52√2, 98, 72√2, 124, 98√2.

Code: 1245 0 72 984 98 98 983 196 98 264 124 72 460 150 98 461 196 98 727 0 72 720 72 72 174 89 55 143 106 58 187 106 72 36 89 55 67 92 58 60 98 58 44 102 54 43 106 54 24 104 52 524 144 0 523 196 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)