  In general relativity, there is a class of solutions that currently do not
have observed analogues, but on which the theory is shaped, giving an
understanding what is fundamentally possible within its framework. Such
solutions include wormholes, tunnels that connect distant regions in spacetime.
Although not a single wormhole has yet been discovered, there is a large number
of works devoted to their study, thanks to which wormholes as a class of
solutions become firmly established in modern science. In this paper, we
consider two topologically nontrivial types of solutions related to wormholes.
First: wormholes that can open and close. In this relation, we will discuss
topological censorship theorems, which under certain conditions prohibit
changing topology. We will also discuss known ways to circumvent these
theorems. Using analytical and numerical methods, as well as visualization, we
will construct an example of an opening and closing wormhole with the
dimensions of the central black hole in the Milky Way galaxy. Our construction
continues the work by Kardashev, Novikov and Shatskiy, in which a static
wormhole with the same parameters was considered. The second type is a
modification of Visser's dihedral wormhole solution for a dynamic case, which
can be considered as a model of a teleportation event.
