diff --git a/engine-proto/Engine.jl b/engine-proto/Engine.jl
index 72b5923..ac9ed35 100644
--- a/engine-proto/Engine.jl
+++ b/engine-proto/Engine.jl
@@ -178,8 +178,17 @@ function realize(ctx::Construction{T}) where T
   # turn relations into equations
   eqns = vcat(
     equation.(ctx.relations),
-    [elt.rel for (_, elt) in eltenum if !isnothing(elt.rel)],
+    [elt.rel for (_, elt) in eltenum if !isnothing(elt.rel)]
   )
+  
+  # add relations to center and orient the construction
+  if !isempty(ctx.points)
+    append!(eqns, [sum(pt.coords[k] for pt in ctx.points) for k in 1:3])
+  end
+  if !isempty(ctx.spheres)
+    append!(eqns, [sum(sph.coords[k] for sph in ctx.spheres) for k in 3:4])
+  end
+  
   Generic.Ideal(coordring, eqns)
 end