Requesting Virtual Mirror for multiple planes, or radial symmetry. Might work like this:
World axes, (simplest solution? maximum 8-fold symmetry, object must be placed near origin or Cartesian planes--if object spans mirrored octants, may optionally indicate side(s) to clip to avoid self-intersecting volumes);
Multiple VM, (arbitrary, object faces--like current VM, multipled--could easily get out of hand, but a flexible solution, esp. if optionally clipped and bridged);
For simple radial symmetry, n-meric symmetry around arbitrary axis, (partially achievable through duplicate, flip, and rotation--[Bryce-style multiple "replicate" would streamline this]--but would benefit from optional clipping and bridging).
Suggest VM operations include optional clipping and bridging to resolve self-intersecting volumes, and to better resolve non-planar faces.
Lastly, VM operations might be permitted to freely create and merge multiple objects, (maybe not so simple for winged-edge format? But might be better than user attempts to correct malformed objects....)
FWIW!
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Of all the different schemes I've been using lately, (Rhino, Silo, and SketchUp), I think SketchUp actually has the most intuitive and flexible way of implementing symmetry: In SU, "components" (kind of like JavaScript prototypes?) propagate edits to any instance to all related instances, while preserving instance-specific transformations (like "flip along axis"). In this way, the SU scheme offers virtually unlimited symmetry, as well as a kind of "local transformation", (probably not the right term).
Silo has "instances", but--like Rhino's history-enabled objects and out-of-the-way "blocks"--it seems only certain transformations and functions are propagated, and specifically to child instances.
FWIW!