Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:236AM GHM

Order: 19

Horizontal side: 236 Vertical side: 236

Elements: 9√2, 18, 18√2, 28, 36, 28√2, 36√2, 52, 50√2, 52√2, 54√2, 80, 82, 86, 68√2, 100, 77√2, 82√2, 100√2.

Code: 1005 0 136 1004 100 136 186 182 218 367 200 236 366 200 200 803 182 138 542 236 164 826 154 82 520 102 138 521 154 138 282 182 110 281 182 138 682 68 68 504 50 86 181 68 86 92 77 77 861 154 86 825 154 0 770 77 77

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)