Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:84AD GHM

Order: 19

Horizontal side: 84 Vertical side: 84

Elements: 4, 4√2, 8, 6√2, 8√2, 12, 16, 12√2, 18, 14√2, 15√2, 18√2, 28, 30, 36, 27√2, 28√2, 42, 42√2.

Code: 425 0 42 424 42 42 276 57 57 150 57 57 122 12 30 121 12 42 62 18 36 284 40 14 283 68 14 47 68 42 40 72 42 87 68 38 80 76 38 186 0 18 365 18 0 167 68 30 303 84 0 185 0 0 144 54 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)