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

Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms