Here's the fastest way I know to unify two polygons.
Step 1 - Put one polygon in the foreground and the other in the background.
Step 2 - In the tools menu, hit drill and pick Z Slice.
Step 3 - Swap the layers ( hit the ' key )
Step 4 - Still in the tools menu, hit drill and pick Z Tunnel.
Step 5 - Cut, swap layers, and paste. ( hit x ' v )
Step 6 - Merge points ( hit m enter enter )
Step 7 - If you have a newer version of Lightwave, skip to step 9.
Otherwise, Select the useless inside points with the lasso.
Step 8 - Zap them. ( hit z )
Step 9 - Select all the polygons ( click one and hit ] ), then in the Polygon menu, hit Merge.
If you have a newer version of Lightwave, there may be points left over, so Select the polygon, cut it ( hit x ), ZAP the points ( hit z ), and paste the polygon back in ( hit v ).
If the polygon isn't showing a normal, hit Merge Points again.
If the problem persists, closely check all the nooks for bad points. If you find any, ZAP them and Merge Points again.
Practise until you can do this really fast. - GLYPH
More 3D Graphics: 
