Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:96AD GHM

Order: 19

Horizontal side: 96 Vertical side: 96

Elements: 2√2, 5√2, 6√2, 10, 11, 12, 12√2, 21, 18√2, 19√2, 28, 32, 36, 38, 28√2, 29√2, 34√2, 36√2, 56.

Code: 385 0 58 364 36 60 363 72 60 182 90 78 124 84 84 123 96 84 64 90 78 563 96 28 24 38 58 213 40 39 327 40 60 292 29 29 194 19 39 101 29 39 52 34 34 111 40 39 340 34 34 284 68 0 283 96 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)