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Labeling Three-Dimensional Graphics

Mathematica provides various options for labeling three-dimensional graphics. Some of these options are directly analogous to those for two-dimensional graphics, discussed in "Labeling Two-Dimensional Graphics". Others are different.
Boxed->Truedraw a cuboidal bounding box around the graphics (default)
Axes->Truedraw x, y and z axes on the edges of the box
Axes->{False,False,True}draw the z axis only
FaceGrids->Alldraw grid lines on the faces of the box
PlotLabel->textgive an overall label for the plot

Some options for labeling three-dimensional graphics.

The default for Graphics3D is to include a box, but no other forms of labeling.
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Setting Axes->True adds x, y and z axes.
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This adds grid lines to each face of the box.
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BoxStyle->stylespecify the style for the box
AxesStyle->stylespecify the style for the axes
AxesStyle->{xstyle,ystyle,zstyle}specify separate styles for each axis

Style options.

This makes the box dashed, and draws axes which are thicker than normal.
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By setting the option Axes->True, you tell Mathematica to draw axes on the edges of the three-dimensional box. However, for each axis, there are in principle four possible edges on which it can be drawn. The option AxesEdge allows you to specify on which edge to draw each of the axes.
AxesEdge->Automaticuse an internal algorithm to choose where to draw all axes
AxesEdge->{xspec,yspec,zspec}give separate specifications for each of the x, y and z axes
Nonedo not draw this axis
Automaticdecide automatically where to draw this axis
{diri,dirj}specify on which of the four possible edges to draw this axis

Specifying where to draw three-dimensional axes.

This draws the x on the edge with larger y and z coordinates, draws no y axis, and chooses automatically where to draw the z axis.
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When you draw the x axis on a three-dimensional box, there are four possible edges on which the axis can be drawn. These edges are distinguished by having larger or smaller y and z coordinates. When you use the specification {diry, dirz} for where to draw the x axis, you can set the diri to be +1 or -1 to represent larger or smaller values for the y and z coordinates.
AxesLabel->Nonegive no axis labels
AxesLabel->zlabelput a label on the z axis
AxesLabel->{xlabel,ylabel,zlabel}put labels on all three axes

Axis labels in three-dimensional graphics.

You can use AxesLabel to label edges of the box, without necessarily drawing scales on them.
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Ticks->Nonedraw no tick marks
Ticks->Automaticplace tick marks automatically
Ticks->{xticks,yticks,zticks}specify tick marks for each axis

Settings for the Ticks option.

You can give the same kind of tick mark specifications in three dimensions as were described for two-dimensional graphics in "Labeling Two-Dimensional Graphics".
FaceGrids->Nonedraw no grid lines on faces
FaceGrids->Alldraw grid lines on all faces
FaceGrids->{face1,face2,...}draw grid lines on the faces specified by the facei
FaceGrids->{{face1,{xgrid1,ygrid1}},...}use xgridi, ygridi to determine where and how to draw grid lines on each face

Drawing grid lines in three dimensions.

Mathematica allows you to draw grid lines on the faces of the box that surrounds a three-dimensional object. If you set FaceGrids->All, grid lines are drawn in gray on every face. By setting FaceGrids->{face1, face2, ...} you can tell Mathematica to draw grid lines only on specific faces. Each face is specified by a list {dirx, diry, dirz}, where two of the diri must be 0, and the third one is +1 or -1. For each face, you can also explicitly tell Mathematica where and how to draw the grid lines, using the same kind of specifications as you give for the GridLines option in two-dimensional graphics.
This draws grid lines only on the top and bottom faces of the box.
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