A twist knot is obtained by linking together the two ends of a twisted loop. Any number of half-twists may be introduced into the loop before linking, resulting in an infinite family of possibilities. The following figures show the first few twist knots:

•  
  One half-twist
  (trefoil knot, 3₁)
•  
  Two half-twists
  (figure-eight knot, 4₁)
•  
  Three half-twists
  (5₂ knot)
•  
  Four half-twists
  (stevedore knot, 6₁)
•  
  Five half-twists
  (7₂ knot)
•  
  Six half-twists
  (8₁ knot)

All twist knots have unknotting number one, since the knot can be untied by unlinking the two ends. Every twist knot is also a 2-bridge knot.^[1] Of the twist knots, only the unknot and the stevedore knot are slice knots.^[2] A twist knot with ${\displaystyle n}$  half-twists has crossing number ${\displaystyle n+2}$ . All twist knots are invertible, but the only amphichiral twist knots are the unknot and the figure-eight knot.

The invariants of a twist knot depend on the number ${\displaystyle n}$  of half-twists. The Alexander polynomial of a twist knot is given by the formula

${\displaystyle \Delta (t)={\begin{cases}{\frac {n+1}{2}}t-n+{\frac {n+1}{2}}t^{-1}&{\text{if }}n{\text{ is odd}}\\-{\frac {n}{2}}t+(n+1)-{\frac {n}{2}}t^{-1}&{\text{if }}n{\text{ is even,}}\\\end{cases}}}$ 

and the Conway polynomial is

${\displaystyle \nabla (z)={\begin{cases}{\frac {n+1}{2}}z^{2}+1&{\text{if }}n{\text{ is odd}}\\1-{\frac {n}{2}}z^{2}&{\text{if }}n{\text{ is even.}}\\\end{cases}}}$ 

When ${\displaystyle n}$  is odd, the Jones polynomial is

${\displaystyle V(q)={\frac {1+q^{-2}+q^{-n}-q^{-n-3}}{q+1}},}$ 

and when ${\displaystyle n}$  is even, it is

${\displaystyle V(q)={\frac {q^{3}+q-q^{3-n}+q^{-n}}{q+1}}.}$