Attaching one face to another I'm just beginning to learn Blender, and I ran into a problem. I ended up with two separate meshes in one object. I want to attach their faces together, as if I had drawn and extruded one from the other. In this example, I have an octagonal prism that I want to attach to the face of a cube. How can I do this without remaking one of the meshes?

What I have now:



I know that one way to work around it would be to simply move the meshes together so they overlap, but then they aren't actually properly attached, and won't move together/etc.
You can use either Boolean modificator (in Object mode) or Intersect tool (in Edit mode). 


Start with cylinder passing through cube.
Cube and cylinder have different amount of vertices, hence cube should be edited in order to have roughly the same shape as cylinder has. It is possible to skip this and create intersection as is, however this way will create Ngons which may be undesired.
One way to change cube accordingly is to bevel it. Select it and press Ctrl+B, 2 segments, low value of Offset. 


Add 1 loopcut per both sides of the cube. Use Connect Vertex Path (J) tool to connect corner vertices.


Select all, in 3D Viewport header choose Mesh > Faces > Intersect tool and in its options (Last Operator panel in the Toolshelf or F6) select Self-Intersect. 


Select all again, press W, choose Remove Doubles. Note that you may need to enter higher threshold for Merge Distance, like 0.02.