Tower vase shroud

What do you call a vase surrounding a vase? A plywood form surrounds around an inner glass vase, cloaking it, protecting it. Standing tall and cylindrically stoic, the tubular form feels like a castle tower, or perhaps a chess rook shielding the king. Yet through twists and blends, elliptical windows unwind and reveal glances of the vase and foliage inside. In Version 1 (shown with dry brush foliage) opposing "columns" of the vase are identical. In Version 2 (shown with green foliage), all four columns are unique. The glass vase is included - a hand-blown, commercial product, easily replaced if you happen to break it - but the glass vase itself is not the artwork.