If the Multiverse in which the Universes are located in allows for this to happen (has a set of laws that allows it), the formation may happen and will be stable for as long as it is unbroken.
This formation can only happen to Multiverses that exist (1-existence), limiting the scope of Imaginary Dodecahedrons to just the Omniverse, which is a very little sample size, when testing out reasons for its reality in the first place.
The Imaginary Dodecahedra themselves, are non-existant (0-existence), and bind together with the existing Universes in seperate dimensions and planes of existence. As the Universes slowly waltz into their respective positions, an Imaginary Dodecahedron is pulled torwards them and inserts itself in, solidifying the Universes' positions and stabilizing the whole structure.
The Universes are now kept in place, nothing happens to the Universes themselves, this Dodecahedron, or the forces of the other Universes, doesn't impact them or the civilizations within.
To remove an Imaginary Dodecahedron from the Universes, simply take away one Universe from the formation. This destabilizes the forces, upon which the whole setup of verses and Dodecahedron will spin approximately 190° in 2 seconds, with the Imaginary Dodecahedron swiftly flying away, and the Universes departing from one another, in all directions, like marbles being spilled on the floor.