Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:296AS GHM

Order: 19

Horizontal side: 296 Vertical side: 296

Elements: 22, 16√2, 19√2, 30, 22√2, 32, 38, 30√2, 32√2, 52, 64, 49√2, 84, 64√2, 116, 148, 116√2, 180, 148√2.

Code: 1805 0 116 1484 148 148 1483 296 148 324 180 116 323 212 116 162 228 132 841 296 148 383 228 94 192 247 113 1167 0 116 1160 116 116 521 168 116 225 168 94 224 190 94 490 247 113 305 168 64 304 198 64 644 232 0 643 296 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)

180
148√2
148
32√2
32
16√2
84
38
19√2
116
116√2
52
22
22√2
49√2
30
30√2
64√2
64