Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:290AB GHM

Order: 19

Horizontal side: 290 Vertical side: 290

Elements: 2, 2√2, 12, 12√2, 24, 19√2, 21√2, 24√2, 42, 46, 36√2, 42√2, 84, 103, 124, 145, 166, 124√2, 145√2.

Code: 1665 0 124 1454 145 145 1453 290 145 214 166 124 190 187 145 1031 290 145 20 168 126 21 170 126 242 194 102 241 194 126 122 206 114 121 206 126 845 206 42 1247 0 124 1240 124 124 461 170 124 366 170 78 424 248 0 423 290 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)

166
145√2
145
21√2
19√2
103
2√2
2
24√2
24
12√2
12
84
124
124√2
46
36√2
42√2
42