Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:96AJ GHM

Order: 19

Horizontal side: 96 Vertical side: 96

Elements: 4, 3√2, 4√2, 6, 8, 12, 16, 18, 20, 24, 18√2, 20√2, 36, 27√2, 40, 42, 30√2, 36√2, 48√2.

Code: 482 48 48 421 42 96 245 42 72 274 69 69 306 66 66 187 42 72 186 42 54 362 96 36 61 66 72 32 69 69 83 48 40 125 48 36 403 40 0 202 60 20 44 44 36 43 48 36 161 60 36 363 96 0 203 60 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)