Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:73AB3of4 GHM

Order: 19

Horizontal side: 73 Vertical side: 73

Elements: 2√2, 4, 3√2, 4√2, 6, 8, 6√2, 8√2, 12, 9√2, 12√2, 19√2, 27, 21√2, 31, 23√2, 27√2, 42, 46.

Code: 465 0 27 421 42 73 122 54 61 311 73 73 123 54 49 192 73 42 92 51 40 64 48 43 63 54 43 34 51 40 86 46 35 216 52 21 46 42 31 85 46 27 275 0 0 274 27 0 43 54 23 230 50 23 24 52 21

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)