Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:216AU GHM

Order: 19

Horizontal side: 216 Vertical side: 216

Elements: 3√2, 6, 6√2, 12, 20, 15√2, 20√2, 30, 40, 30√2, 31√2, 37√2, 40√2, 68, 88, 108, 88√2, 128, 108√2.

Code: 1285 0 88 1084 108 108 1083 216 108 204 128 88 203 148 88 312 179 77 681 216 108 887 0 88 880 88 88 304 118 58 303 148 58 370 179 77 154 133 43 123 148 46 36 133 43 65 136 40 64 142 40 404 176 0 403 216 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)