Detailed theme with Ticks in Plot3D do not work

Question

I need to divide the axis period when plotting and use Detailed theme

For example,

Plot[x, {x, 0, 1}, 
 Ticks -> {0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1}, 
 PlotTheme -> "Detailed"]

But when using the three-dimensional plotting (Plot3D) do not work with the theme.

Plot3D[x y, {x, 0, 1}, {y, 0, 
  1}, {Ticks -> {{0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 
     1}, {0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1}}}, 
 PlotTheme -> "Detailed"]

what is the reason?

Is there a solution to operate the theme by dividing the axis?

Answer 1

You have to specify the Facegrids yourself, f.e. like this:

Plot3D[x y, {x, 0, 1}, {y, 0, 1},
 Ticks -> {{0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1}, {0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1}},
 FaceGrids -> {
   {{0, 1, 0}, {Range[0, 1, 0.1], Range[0, 1, 0.1]}},
   {{-1, 0, 0}, {Range[0, 1, 0.1], Range[0, 1, 0.1]}}},
 ImageSize -> Large,
 PlotTheme -> "Detailed"]

Answer 2

You can get the same look as the 2D graph by specifying the ticks for all three axes. Like so:

Plot3D[x y, {x, 0, 1}, {y, 0, 1},
  BoxRatios -> 1,
  Ticks -> ConstantArray[Range[0, 1, .2], 3],
  PlotTheme -> "Detailed"]

Giving the BoxRatios option isn't necessary. I just think it makes the plot look better.