Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:216AS GHM

Order: 19

Horizontal side: 216 Vertical side: 216

Elements: 5√2, 8, 18, 13√2, 20, 18√2, 26, 28, 20√2, 26√2, 40, 40√2, 62, 68, 88, 108, 88√2, 128, 108√2.

Code: 1285 0 88 1084 108 108 1083 216 108 204 128 88 203 148 88 285 148 80 681 216 108 887 0 88 880 88 88 264 114 62 263 140 62 132 153 75 81 148 88 54 153 75 180 158 80 181 176 80 402 216 40 621 176 62 403 216 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)