Object mode, select, “set origin” from the tool shelf or ctrl+alt+shift+C -> origin to geometry. Switch center option to bounds center from the operator panel on the bottom of the tool shelf
Shift+S -> cursor to selected
Add a cube (shift+A, or any other place primitives can be added)
Have the added cube selected, then shift+select your original object so it’s active, then right click on the dimensions field on the 3d view properties (hotkey N) and choose “copy to selected”. The cube should now be positioned and the same size as the bounding box of your original object, but have to select the cube and ctrl+A -> scale to have unscaled version of it.
How to make it not cast shadows depends on the used render engine, which wasn’t mentioned, and the wanted appearance is not clear. If the default render engine is used (blender render) and an actual wire should be rendered, could add a material and then switch its type to wire and toggle cast and maybe receive off from its shadow options.
Since this is the support forum, should probably mention that the most basic mesh element is a vertex, not “vertice”.