Drawing Rotated views while ignoring the Bounding box

I am trying to make an animation of a rotating cube using the following code:

cube = GraphicsComplex[
{{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}},
Polygon[{{1, 2, 4, 3}, {5, 6, 8, 7}, {1, 2, 6, 5}, {3, 4, 8, 7}, {1, 3, 7, 5}, {2, 4, 8, 6}}]
]

cubes = Table[
Graphics3D[{Rotate[cube, x, {1, 1, 1}, {0, 0, 0}]}, 
ViewPoint -> {3, 1/2, -2}, ViewVertical -> {1, 1, 1}, 
Boxed -> False], {x, 0, 2 Pi/3 - Pi/48, Pi/24}]

However, as the cube rotates, the bounding box (which is not drawn because Boxed->False) causes the image of the cube to be shrunk to fit the larger bounding box in the field of view. Is there a way to keep the scale constant and not vary with the varying size of the bounding box?

I’ve gone through the list of options for Graphics3D, yet none seem to help.

---

Edit:

Heike’s answer works like a charm! For those interested, here is the finished code, used to create the illustration for this answer on math.SE.

cube =
GraphicsComplex[
{{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}},
Polygon[{{1, 2, 4, 3}, {5, 6, 8, 7}, {1, 2, 6, 5}, {3, 4, 8, 7}, {1, 3, 7, 5}, {2, 4, 8, 6}}]
];

envelope[t_] := If[t < 1, t, If[t < 2, Sqrt[(2 t - 3)^2 + 3]/2, 3 - t]]

lozenge = 
Rotate[
RevolutionPlot3D[{Sqrt[2/3] envelope[t], t/Sqrt[3]}, {t, 0, 3}, MaxRecursion -> 5][[1]],
{{0, 0, 1}, {1, 1, 1}}];

enveloped = 
Table[
Graphics3D[{Rotate[cube, x, {1, 1, 1}, {0, 0, 0}],  Opacity[1/2], lozenge},
ViewVector -> {3, 1/2, -2}, ViewAngle -> 30 Degree, ViewCenter -> {1/2, 1/2, 1/2}, 
ViewVertical -> {1, 1, 1}, Boxed -> False, ImageSize -> 300],
{x, 0, 2 Pi/3 - Pi/48, Pi/24}];

Export["enveloped.gif", enveloped, "GraphicsList", "DisplayDurations" -> {.05}]

---

Migration to Newer Versions

With changes to Mathematica, the code above does not parse. When I fixed the code so it parsed, it renders on screen nicely, but upon Export, it rendered pretty badly (at least on the Mac Powerbook, which has 144 dpi screen resolution and tells some applications to render at 144 and others to render at 72 dpi). I was able to adjust some parameters in the code and in the Export statement to get an almost identical output.

cube =
GraphicsComplex[
{{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}},
Polygon[{{1, 2, 4, 3}, {5, 6, 8, 7}, {1, 2, 6, 5}, {3, 4, 8, 7}, {1, 3, 7, 5}, {2, 4, 8, 6}}]
];

envelope[t_] := If[t < 1, t, If[t < 2, Sqrt[(2 t - 3)^2 + 3]/2, 3 - t]]

lozenge = 
Rotate[
RevolutionPlot3D[{Sqrt[2/3] envelope[t], t/Sqrt[3]}, {t, 0, 3}, MaxRecursion -> 5,
PlotTheme -> "Classic",Exclusions -> None, MeshStyle -> {Thickness[1/144]}][[1]],
{{0, 0, 1}, {1, 1, 1}}];

enveloped = 
Table[
Graphics3D[{EdgeForm[Thickness[1/144]], 
Rotate[cube, x, {1, 1, 1}, {0, 0, 0}], Opacity[1/2], lozenge}, ViewVector -> {3, 1/2, -2},
ViewAngle -> 30 Degree, ViewCenter -> {1/2, 1/2, 1/2}, ViewVertical -> {1, 1, 1},
Background -> None, Boxed -> False, ImageSize -> 300, Lighting -> "Classic"],
{x, 0, 2 Pi/3 - Pi/48, Pi/24}]

Export["enveloped.gif", enveloped, "GraphicsList", "DisplayDurations" -> .05,
"AnimationRepetitions" -> Infinity, ImageSize -> 300, ImageResolution -> 144]

(* For the high resolution image, we need to change the Thickness Directive to *)
(* Thickness[1/288] then *)

Export["enveloped2.gif", enveloped, "GraphicsList", "DisplayDurations" -> .05,
"AnimationRepetitions" -> Infinity, ImageSize -> 600, ImageResolution -> 144]

cubes = Table[
  Graphics3D[{Rotate[cube, x, {1, 1, 1}, {0, 0, 0}]}, 
   ViewVector -> {3, 1/2, -2}, 
   ViewAngle -> 35 Degree,
   ViewCenter -> {.5, .5, .5},
   ViewVertical -> {1, 1, 1}, Boxed -> False],
  {x, 0, 2 Pi/3 - Pi/48, Pi/24}]