Why don't I see all the planes in the ChromaticityPlot3D?

Question

Using the default setting, I can have my desired ChromaticityPlot3D as

ChromaticityPlot3D["LAB", "LAB"];

However, the problem with this plot is that it has (probably) the PlotRange as {{0.,1.},{-1.3,1.3},{-1.3,1.3}} and I don't want these additional ranges beyond {-1.,1.}.

Therefore, when I set the PlotRange as {{0.,1.},{-1.,1.},{-1.,1.}} I can see only the top and the bottom planes (using the default view setting).

Is it possible to have the PlotRange as {{0.,1.},{-1.,1.},{-1.,1.}} and still see the ChromaticityPlot3D as it is seen with the default settings?

Edit 1 Or may be the ranges for the CIE LAB is considered as {0,1},{-1.28,1.27},{-1.28,1.27}

Answer 1

cp = ChromaticityPlot3D["LAB", "LAB"]

PlotRange[cp]

{{2.22045*10^-16, 1.}, {-1.28, 1.28}, {-1.28, 1.28}}

cp2 = cp /.  GraphicsComplex[x_, p__] :>  GraphicsComplex[ 
  Transpose[{#, Clip[#2, {-1, 1}], Clip[#3, {-1, 1}]} & @@ Transpose[x]], p]

PlotRange[cp2]

{{2.22045*10^-16, 1.}, {-1., 1.}, {-1., 1.}}

Answer 2

We can plot our own version:

RegionPlot3D[
  -1 <= a <= 1 && -1 <= b <= 1 && 0 <= L <= 1,
  {a, -1, 1}, {b, -1, 1}, {L, 0, 1}, 
  Axes -> True,
  AxesLabel -> SuperStar /@ {"a", "b", "L"},
  BoxRatios -> {1, 1, 1}, 
  ColorFunction -> Function[{a, b, L}, LABColor[L, a, b]], 
  ColorFunctionScaling -> False, 
  Lighting -> "Neutral", 
  Mesh -> None
]