Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:106AA GHM

Order: 19

Horizontal side: 106 Vertical side: 106

Elements: 6√2, 14, 13√2, 14√2, 16√2, 17√2, 26, 28, 20√2, 32, 34, 36, 38, 40, 42, 32√2, 34√2, 36√2, 38√2.

Code: 425 0 64 364 36 70 176 55 89 347 72 106 346 72 72 130 55 89 66 36 70 267 42 76 403 68 36 382 106 38 322 32 32 281 28 64 142 42 50 141 42 64 383 106 0 204 48 16 363 68 0 323 32 0 162 48 16

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)