Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:132AB GHM

Order: 19

Horizontal side: 132 Vertical side: 132

Elements: 4, 3√2, 4√2, 6, 8, 6√2, 11√2, 15√2, 22, 17√2, 22√2, 23√2, 44, 52, 40√2, 44√2, 66, 55√2, 66√2.

Code: 665 0 66 664 66 66 406 92 92 156 77 77 172 109 75 110 77 77 230 109 75 445 0 22 444 44 22 83 88 58 42 92 62 43 92 58 36 77 55 65 80 52 64 86 52 550 77 55 521 132 52 225 0 0 224 22 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)