Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:150AF2of2 GHM

Order: 19

Horizontal side: 150 Vertical side: 150

Elements: 8√2, 12, 9√2, 16, 12√2, 18, 16√2, 24, 18√2, 32, 24√2, 34, 48, 34√2, 66, 68, 58√2, 84, 75√2.

Code: 845 0 66 754 75 75 586 92 92 80 92 92 96 75 75 167 84 84 160 100 84 327 84 68 683 116 0 342 150 34 667 0 66 180 66 66 181 84 66 483 48 0 242 72 24 241 72 48 122 84 36 121 84 48 343 150 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)