Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:218AH GHM

Order: 19

Horizontal side: 218 Vertical side: 218

Elements: 12, 12√2, 17, 21, 24, 17√2, 19√2, 21√2, 24√2, 42, 46, 48, 42√2, 67, 88, 109, 88√2, 130, 109√2.

Code: 1305 0 88 1094 109 109 1093 218 109 214 130 88 213 151 88 192 170 90 671 218 109 246 146 66 485 170 42 887 0 88 880 88 88 461 134 88 172 151 71 171 151 88 126 134 54 245 146 42 125 134 42 424 176 0 423 218 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)

130
109√2
109
21√2
21
19√2
67
24√2
48
88
88√2
46
17√2
17
12√2
24
12
42√2
42