Can I line the mesh lines on a `RegionPlot3D` up with integer values of the axes?

Question

(Sorry if this is a duplicate, I searched briefly and didn't find anything.)

I have region plots in 3D like:

RegionPlot3D[x <= 5 && y + z <= 7 && x + y <= 8 && z <= 5, {x, 0, 10}, {y, 0, 10}, {z, 0, 10}]

I have been messing around with the Mesh parameter trying to get the mesh lines to correspond to unit lengths along the axes. But when features of the plot change (e.g., the constants 5, 7, 8) the mesh no longer shows me integer cross-sections of the axes.

Is there a value of Mesh, or perhaps MeshFunctions, that will place the mesh lines onto integer values of the axes?

Answer 1

RegionPlot3D[x <= 5 && y + z <= 7 && x + y <= 8 && z <= 5, {x, 0, 10}, {y, 0, 10}, {z, 0, 10},
 Mesh -> {{1, 2, 3, 4, 5}, {1, 2, 3, 4, 5}}]

or

RegionPlot3D[x <= 5 && y + z <= 7 && x + y <= 8 && z <= 5, {x, 0, 10}, {y, 0, 10}, {z, 0, 10},
 Mesh -> 10, MeshFunctions -> {Floor[#1] &, Floor[#2] &}]