Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:84AJ GHM

Order: 19

Horizontal side: 84 Vertical side: 84

Elements: 2, 2√2, 4, 3√2, 4√2, 12, 10√2, 12√2, 14√2, 23, 24, 17√2, 25, 28, 21√2, 24√2, 42, 36√2, 42√2.

Code: 425 0 42 424 42 42 366 48 48 106 38 38 242 72 24 212 21 21 174 17 25 140 34 42 44 38 38 30 20 28 281 48 28 41 21 25 22 23 23 21 23 25 255 23 0 243 72 0 122 84 12 233 23 0 123 84 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)