Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:43AA GHM

Order: 19

Horizontal side: 43 Vertical side: 43

Elements: 2, 3√2, 6, 5√2, 8, 6√2, 7√2, 10, 11, 12, 13, 14, 10√2, 11√2, 13√2, 20, 15√2, 22, 16√2.

Code: 162 16 27 154 15 28 123 30 31 132 43 30 131 43 43 36 15 28 65 18 25 64 24 25 143 30 17 203 43 10 56 11 22 25 16 25 87 16 25 116 0 11 225 11 0 74 23 10 115 0 0 104 33 0 103 43 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)