Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:108AE GHM

Order: 19

Horizontal side: 108 Vertical side: 108

Elements: 4√2, 8, 7√2, 8√2, 14, 16, 13√2, 16√2, 26, 28, 20√2, 26√2, 28√2, 40, 34√2, 35√2, 40√2, 41√2, 60.

Code: 412 41 67 344 34 74 206 48 88 407 68 108 406 68 68 143 48 74 605 48 28 74 41 67 356 13 39 130 13 39 165 48 12 164 64 12 280 80 28 281 108 28 267 0 26 260 26 26 85 48 4 84 56 4 44 52 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)