International Guild of Knot Tyers Forum

General => New Knot Investigations => Topic started by: X1 on March 04, 2013, 03:13:04 AM

Title: Yet another Pretzel-to-Pretzel bend.
Post by: X1 on March 04, 2013, 03:13:04 AM
   The interweaved Pretzel-shaped links of the bend shown at the first and second attached pictures are "symmetric" (S) - in the sense that the two legs leave the central bight from different sides. On the contrary, each Pretzel at the similar bend presented some time ago ( shown at the thirsd and fourth attached pictures ), is "one-sided"  / "a-symmetric" (aS). For other a-symmetric Pretzel-to-Pretzel bends, see (1), Replies#7, #8 and #9. ( Mike s "fancy bend", Axis knot (M. A22), Axis B knot ). Another similar bend is one ( the first, bend B ) of the two bends shown at (2).

1. http://igkt.net/sm/index.php?topic=3585
2. http://igkt.net/sm/index.php?topic=3671.msg22197#msg22197
Title: Re: Yet another Pretzel-to-Pretzel bend.
Post by: xarax on January 28, 2014, 01:29:30 PM
  The representation of the pattern of a relatively simple side-by-side Pretzel-to-Pretzel bend can have two forms - as shown at the attached pictures. In contrast to the more convoluted side-to-side fig.8-to-fig.8 bends (1), these bends can not be perfectly symmetric, because, although the topology of the links can be the same, the geometry can not but differ : if the Standing parts are placed symmetrically to each other, their path through the knot s nub would be slightly different (2). ( This is the reason I had always placed the Pretzel-to-Pretzel links face-to-face - in the same way as the Jug sling bend / Axis knot / Mike s fancy bend, for example ).

1. http://igkt.net/sm/index.php?topic=3148.msg22234#msg22234
2. http://igkt.net/sm/index.php?topic=4756.msg30812#msg30812