diff --git a/docs/src/PolyhedralGeometry/intro.md b/docs/src/PolyhedralGeometry/intro.md
index f185306a969b..f393093a77b3 100644
--- a/docs/src/PolyhedralGeometry/intro.md
+++ b/docs/src/PolyhedralGeometry/intro.md
@@ -177,7 +177,7 @@ fan for its construction, see [`polyhedral_fan`](@ref).
 Lower dimensional polyhedral objects can be visualized through polymake's backend.
 
 ```@docs
-visualize(P::PolyhedralObject{T}) where T<:Union{QQFieldElem, Float64}
+visualize(P::Union{Polyhedron{T}, Cone{T}, PolyhedralFan{T}, PolyhedralComplex{T}}) where T<:Union{QQFieldElem, Float64}
 ```
 
 
diff --git a/src/PolyhedralGeometry/visualization.jl b/src/PolyhedralGeometry/visualization.jl
index e27999a9c580..54b38f0874e4 100644
--- a/src/PolyhedralGeometry/visualization.jl
+++ b/src/PolyhedralGeometry/visualization.jl
@@ -1,5 +1,5 @@
 @doc raw"""
-    visualize(P::Union{Polyhedron{T}, Cone{T}, PolyhedralFan{T}, PolyhedralComplex{T}}) where T<:Union{QQFieldElem, Float64}
+    visualize(P::Union{Polyhedron{T}, Cone{T}, PolyhedralFan{T}, PolyhedralComplex{T}, SubdivisionOfPoints{T}}) where T<:Union{QQFieldElem, Float64}
 
 Visualize a polyhedral object of dimension at most four (in 3-space).
 In dimensions up to 3 a usual embedding is shown.
@@ -7,20 +7,33 @@ Four-dimensional polytopes are visualized as a Schlegel diagram, which is a proj
 
 In higher dimensions there is no standard method; use projections to lower dimensions or try ideas from [GJRW10](@cite).
 """
-function visualize(P::PolyhedralObject{T}) where T<:Union{QQFieldElem, Float64}
+function visualize(P::Union{Polyhedron{T}, Cone{T}, PolyhedralFan{T}, PolyhedralComplex{T}}) where T<:Union{QQFieldElem, Float64}
   d = ambient_dim(P)
   b = P isa Polyhedron
-  if d < 4 || (d == 4 && b && dim(P) == 4)
-    # polymake will by default use 0:n-1 as ray labels so we assign labels
-    # starting from 1 here if there are no labels yet
-    # (note: labels are mutable, i.e. they can be changed again later)
-    if !Polymake.exists(pm_object(P), "RAY_LABELS")
-      pm_object(P).RAY_LABELS = string.(1:Oscar.pm_object(P).N_RAYS)
-    end
-    pmo = pm_object(P)
-    Polymake.visual(pmo)
+  if b && d == 4
+    @req is_fulldimensional(P) "Can only visualize full-dimensional $(typeof(P)) of ambient dimension $d"
   else
-    d == 4 && b && throw(ArgumentError("Can only visualize full-dimensional $(typeof(P)) of ambient dimension $d"))
-    throw(ArgumentError("Can not visualize $(typeof(P)) of ambient dimension $d. Supported range: 1 <= d <= $(3 + b)"))
+    @req d < 4  "Can not visualize $(typeof(P)) of ambient dimension $d. Supported range: 1 <= d <= $(3 + b)"
   end
+  # polymake will by default use 0:n-1 as ray labels so we assign labels
+  # starting from 1 here if there are no labels yet
+  # (note: labels are mutable, i.e. they can be changed again later)
+  if !Polymake.exists(pm_object(P), "RAY_LABELS")
+    pm_object(P).RAY_LABELS = string.(1:Oscar.pm_object(P).N_RAYS)
+  end
+  pmo = pm_object(P)
+  Polymake.visual(pmo)
+end
+
+function visualize(P::SubdivisionOfPoints{T}) where T<:Union{QQFieldElem, Float64}
+  d = ambient_dim(P)
+  @req d <= 3 "Can not visualize $(typeof(P)) of ambient dimension $d. Supported range: 1 <= d <= 3"
+  # polymake will by default use 0:n-1 as labels so we assign labels
+  # starting from 1 here if there are no labels yet
+  # (note: labels are mutable, i.e. they can be changed again later)
+  if !Polymake.exists(pm_object(P), "POINT_LABELS")
+    pm_object(P).POINT_LABELS = string.(1:Oscar.pm_object(P).N_POINTS)
+  end
+  pmo = pm_object(P)
+  Polymake.visual(pmo)
 end