Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:304AR GHM

Order: 19

Horizontal side: 304 Vertical side: 304

Elements: 2√2, 4, 4√2, 8, 12, 14, 14√2, 28, 21√2, 34, 42, 76, 76√2, 110, 97√2, 152, 110√2, 194, 152√2.

Code: 1945 0 110 1524 152 152 1523 304 152 421 194 152 285 194 124 341 228 152 767 228 152 766 228 76 145 194 110 144 208 110 20 222 124 123 220 110 47 220 122 40 224 122 87 220 118 216 207 97 1105 0 0 1104 110 0 970 207 97

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)