Is there any way to take my circular vertices, and make them square so that they match my cube? I want it to be a cone with a circular base and a rectangular top.
I'd suggest creating such a cone by starting with a cube and using the subdivide and circile tools:
- Add a cube.
- Select the bottom face.
- Subdivide 3 times (don't worry about the Ngons above, we'll take care of them later). Use the specials menu (W > Subdivide) or the Tools shelf.
- Use the Looptools > Circle tool to turn the base into a circle (W > Looptools > Circle). If you don't see the Looptools activate the addon through the User Preferences Window (CtrlAltU > Addons Tab).
- Select the top face and scale down as much as you need.
- Select the central faces (everything except the top and bottom faces).
- Triangulate (CtrlT)
After subdividing the cube/square to match the circle subdivisions number (with W-->Subdivide) you may try to join vertices using the Bridge Tool. Select the vertices with Alt+RMB as pictured below, hit Spacebar, type 'bridge edge loops' and then dissolve the newly created edgeloop. Select it with Alt+RMB, then hit X-->Dissolve Edges. At the very end select the vertices of a square, hit Spacebar, type Grid Fill and set up the settings as pictured below.