Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:122CD1of4 GHM

Order: 19

Horizontal side: 122 Vertical side: 122

Elements: 1, 1√2, 2, 2√2, 3√2, 7, 7√2, 10, 10√2, 17√2, 27, 34, 27√2, 44, 34√2, 61, 44√2, 78, 61√2.

Code: 785 0 44 614 61 61 613 122 61 174 78 44 270 95 61 271 122 61 447 0 44 440 44 44 74 51 37 73 58 37 105 58 34 104 68 34 34 54 34 10 57 37 11 58 37 20 56 36 21 58 36 344 88 0 343 122 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)

78
61√2
61
17√2
27√2
27
44
44√2
7√2
7
10
10√2
3√2
1√2
1
2√2
2
34√2
34