# Is there a formal name for this type of knot?

My (undergrad) research group and I were working with this one specific class of knots, and we don't know quite how to search up their qualities to find out if they have a name.

Basically, they are knots with only one twist in their center, with some odd number x of crossings in their center twist. The trefoil is one such knot, with x=3. The next colorable one is at x=9. I don't think we're talking about Twist Knots, of which the Trefoil is also one such knot, because to my untrained eye the two look different. See below for x=9 "8-Bigon Twisty Knot" as we preliminarily called it:

knot with one twist and 9 crossings

So, do you know if these kinds of knots have a name? Or should we just call them "knot with one twist and x crossings"...

• The pictured knot is the $(2,9)$ torus knot. If there is one twist and $k$ crossings, then it is the $(2,k)$ torus knot (or link). With more than one twist region, perhaps it would be a pretzel knot or link, depending on how the twist regions are arranged. Commented Mar 6, 2018 at 1:30