Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:304AU GHM

Order: 19

Horizontal side: 304 Vertical side: 304

Elements: 4√2, 8, 8√2, 16, 13√2, 24, 26, 28, 28√2, 56, 42√2, 68, 84, 110, 97√2, 152, 110√2, 194, 152√2.

Code: 1945 0 110 1524 152 152 1523 304 152 424 194 110 163 236 136 82 244 144 681 304 152 83 244 136 42 248 140 286 220 112 565 248 84 263 220 110 247 220 136 285 220 84 1105 0 0 1104 110 0 136 207 97 970 207 97 841 304 84

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)