is vertex visible ?

This is how I would do it - slightly different from your versions. Note that one issue you may have is using updatenormals on the cube as this command averages the normals of shared verts. In this case as the normals are the same for each vertice in the triangle it's probably quicker to just loop throught the triangles rather than the verts.

	;setup graphics
	Graphics3D 800, 600, 0, 2
	SetBuffer BackBuffer()
	
	;enable wireframe	
	WireFrame 1

	;create camera	
	camera = CreateCamera()
	MoveEntity camera, 0, 0, -5
	
	;create pivot for camera	
	campiv = CreatePivot()
	EntityParent camera, campiv
	
	;create cube	
	cube = CreateCube()
	
	;Omit this Line as UpdateNormals averages cooexistent vertices
	;UpdateNormals cube
	s = GetSurface(cube, 1)
	
	Repeat
		
		;turn camera
		TurnEntity campiv, 0, 1, 0
		RenderWorld
		
		;loop through all triangles		
		For v = 0 To CountVertices( s ) - 1
		
			;get global vertex position
			TFormPoint VertexX( s, v ) , VertexY( s, v ), VertexZ( s, v ) , cube, 0
			;get direction vector from camera to vertex
			Cx# = TFormedX() - EntityX( camera, 1 )
			Cy# = TFormedY() - EntityY( Camera, 1 )
			Cz# = TFormedZ() - EntityZ( camera, 1 )
			;tform normal into Global coords 
			TFormNormal VertexNX( s, v ) , VertexNY( s, v ) , VertexNZ( s, v ), cube, 0
			;dot product
			Dot# = Cx * TFormedX() + Cy * TFormedY() + Cz * TFormedZ()
			
			If Dot< 0 			
				TFormPoint VertexX( s, v ) , VertexY( s, v) , VertexZ( s, v ), cube, 0
				CameraProject camera, TFormedX(), TFormedY(), TFormedZ() 
				Color 255,0,0
				Oval ProjectedX()-1, ProjectedY()-1, 3, 3
			End If
			
		Next
							
		Flip
		
	Until KeyHit(1)
	
	End

Stevie