Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:268AC GHM

Order: 19

Horizontal side: 268 Vertical side: 268

Elements: 1√2, 2, 2√2, 4, 6, 7√2, 10√2, 20, 20√2, 40, 40√2, 74, 80, 94, 114, 134, 154, 114√2, 134√2.

Code: 1545 0 114 1344 134 134 1343 268 134 204 154 114 203 174 114 102 184 124 941 268 134 26 182 122 45 184 120 16 181 121 25 182 120 70 181 121 61 188 120 805 188 40 1147 0 114 1140 114 114 741 188 114 404 228 0 403 268 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)