  Given a transitive permutation group, a fundamental object for studying its
higher transitivity properties is the permutation action of its isotropy
subgroup. We reverse this relationship and introduce a universal construction
of infinite permutation groups that takes as input a given system of
imprimitivity for its isotropy subgroup.
  This produces vast families kaleidoscopic groups. We investigate their
algebraic properties, such as simplicity and oligomorphy; their homological
properties, such as acyclicity or contrariwise large Schur multipliers; their
topological properties, such as unique polishability.
  Our construction is carried out within the framework of homeomorphism groups
of topological dendrites.
