Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:208AV GHM

Order: 19

Horizontal side: 208 Vertical side: 208

Elements: 1√2, 2, 2√2, 4, 4√2, 8, 14, 15√2, 22, 30, 26√2, 52, 52√2, 74, 82, 74√2, 78√2, 134, 104√2.

Code: 1345 0 74 1044 104 104 786 130 130 260 130 130 301 134 104 152 149 89 221 156 104 522 208 52 10 149 89 143 148 74 27 148 88 20 150 88 47 148 86 40 152 86 87 148 82 823 156 0 745 0 0 744 74 0 523 208 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)