diff --git a/Project.toml b/Project.toml
index eedd899f7591..cec494303ee9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -36,7 +36,7 @@ LazyArtifacts = "1.6"
 Markdown = "1.6"
 Nemo = "0.45.5"
 Pkg = "1.6"
-Polymake = "0.11.14"
+Polymake = "0.11.19"
 Random = "1.6"
 RandomExtensions = "0.4.3"
 Serialization = "1.6"
diff --git a/src/Combinatorics/Graphs/functions.jl b/src/Combinatorics/Graphs/functions.jl
index 46ebfed592ff..17d9a999fc2c 100644
--- a/src/Combinatorics/Graphs/functions.jl
+++ b/src/Combinatorics/Graphs/functions.jl
@@ -342,7 +342,7 @@ function reverse(e::Edge)
 end
 
 
-struct EdgeIterator
+mutable struct EdgeIterator
     pm_itr::Polymake.GraphEdgeIterator{T} where {T <: Union{Directed, Undirected}}
     l::Int64
 end
@@ -350,7 +350,7 @@ Base.length(eitr::EdgeIterator) = eitr.l
 Base.eltype(::Type{EdgeIterator}) = Edge
 
 function Base.iterate(eitr::EdgeIterator, index = 1)
-    if index > eitr.l
+    if eitr.l == 0 || Polymake.isdone(eitr.pm_itr)
         return nothing
     else
         e = Polymake.get_element(eitr.pm_itr)
@@ -358,6 +358,7 @@ function Base.iterate(eitr::EdgeIterator, index = 1)
         t = Polymake.last(e)
         edge = Edge(s+1, t+1)
         Polymake.increment(eitr.pm_itr)
+        eitr.l -= 1
         return (edge, index+1)
     end
 end
diff --git a/src/PolyhedralGeometry/Polyhedron/properties.jl b/src/PolyhedralGeometry/Polyhedron/properties.jl
index 41b276fce644..98ab089f37ed 100644
--- a/src/PolyhedralGeometry/Polyhedron/properties.jl
+++ b/src/PolyhedralGeometry/Polyhedron/properties.jl
@@ -731,7 +731,7 @@ julia> dim(P)
 dim(P::Polyhedron) = Polymake.polytope.dim(pm_object(P))::Int
 
 @doc raw"""
-    lattice_points(P::Polyhedron{QQFieldElem})
+    lattice_points(P::Polyhedron)
 
 Return the integer points contained in the bounded polyhedron `P`.
 
@@ -757,7 +757,7 @@ julia> matrix(ZZ, lattice_points(S))
 [2   0]
 ```
 """
-function lattice_points(P::Polyhedron{QQFieldElem})
+function lattice_points(P::Polyhedron)
   @req pm_object(P).BOUNDED "Polyhedron not bounded"
   return SubObjectIterator{PointVector{ZZRingElem}}(
     P, _lattice_point, size(pm_object(P).LATTICE_POINTS_GENERATORS[1], 1)
@@ -765,7 +765,7 @@ function lattice_points(P::Polyhedron{QQFieldElem})
 end
 
 _lattice_point(
-  T::Type{PointVector{ZZRingElem}}, P::Polyhedron{QQFieldElem}, i::Base.Integer
+  T::Type{PointVector{ZZRingElem}}, P::Polyhedron, i::Base.Integer
 ) = point_vector(ZZ, @view pm_object(P).LATTICE_POINTS_GENERATORS[1][i, 2:end])::T
 
 _point_matrix(::Val{_lattice_point}, P::Polyhedron; homogenized=false) =
@@ -774,7 +774,7 @@ _point_matrix(::Val{_lattice_point}, P::Polyhedron; homogenized=false) =
 _matrix_for_polymake(::Val{_lattice_point}) = _point_matrix
 
 @doc raw"""
-    interior_lattice_points(P::Polyhedron{QQFieldElem})
+    interior_lattice_points(P::Polyhedron)
 
 Return the integer points contained in the interior of the bounded polyhedron
 `P`.
@@ -792,7 +792,7 @@ julia> matrix(ZZ, interior_lattice_points(c))
 [0   0   0]
 ```
 """
-function interior_lattice_points(P::Polyhedron{QQFieldElem})
+function interior_lattice_points(P::Polyhedron)
   @req pm_object(P).BOUNDED "Polyhedron not bounded"
   return SubObjectIterator{PointVector{ZZRingElem}}(
     P, _interior_lattice_point, size(pm_object(P).INTERIOR_LATTICE_POINTS, 1)
@@ -800,7 +800,7 @@ function interior_lattice_points(P::Polyhedron{QQFieldElem})
 end
 
 _interior_lattice_point(
-  T::Type{PointVector{ZZRingElem}}, P::Polyhedron{QQFieldElem}, i::Base.Integer
+  T::Type{PointVector{ZZRingElem}}, P::Polyhedron, i::Base.Integer
 ) = point_vector(ZZ, @view pm_object(P).INTERIOR_LATTICE_POINTS[i, 2:end])::T
 
 _point_matrix(::Val{_interior_lattice_point}, P::Polyhedron; homogenized=false) =
@@ -813,7 +813,7 @@ _point_matrix(::Val{_interior_lattice_point}, P::Polyhedron; homogenized=false)
 _matrix_for_polymake(::Val{_interior_lattice_point}) = _point_matrix
 
 @doc raw"""
-    boundary_lattice_points(P::Polyhedron{QQFieldElem})
+    boundary_lattice_points(P::Polyhedron)
 
 Return the integer points contained in the boundary of the bounded polyhedron
 `P`.
@@ -841,7 +841,7 @@ julia> matrix(ZZ, boundary_lattice_points(c))
 [ 1    0    0]
 ```
 """
-function boundary_lattice_points(P::Polyhedron{QQFieldElem})
+function boundary_lattice_points(P::Polyhedron)
   @req pm_object(P).BOUNDED "Polyhedron not bounded"
   return SubObjectIterator{PointVector{ZZRingElem}}(
     P, _boundary_lattice_point, size(pm_object(P).BOUNDARY_LATTICE_POINTS, 1)
@@ -849,7 +849,7 @@ function boundary_lattice_points(P::Polyhedron{QQFieldElem})
 end
 
 _boundary_lattice_point(
-  T::Type{PointVector{ZZRingElem}}, P::Polyhedron{QQFieldElem}, i::Base.Integer
+  T::Type{PointVector{ZZRingElem}}, P::Polyhedron, i::Base.Integer
 ) = point_vector(ZZ, @view pm_object(P).BOUNDARY_LATTICE_POINTS[i, 2:end])::T
 
 _point_matrix(::Val{_boundary_lattice_point}, P::Polyhedron; homogenized=false) =
diff --git a/src/PolyhedralGeometry/helpers.jl b/src/PolyhedralGeometry/helpers.jl
index b1526c7b62f3..0df7324f58f6 100644
--- a/src/PolyhedralGeometry/helpers.jl
+++ b/src/PolyhedralGeometry/helpers.jl
@@ -676,6 +676,14 @@ end
 
 # oscarnumber helpers
 
+function Polymake._fieldelem_to_floor(e::Union{EmbeddedNumFieldElem,QQBarFieldElem})
+  return BigInt(floor(ZZRingElem, e))
+end
+
+function Polymake._fieldelem_to_ceil(e::Union{EmbeddedNumFieldElem,QQBarFieldElem})
+  return BigInt(ceil(ZZRingElem, e))
+end
+
 function Polymake._fieldelem_to_rational(e::EmbeddedNumFieldElem)
   return Rational{BigInt}(QQ(e))
 end
diff --git a/src/Serialization/polymake.jl b/src/Serialization/polymake.jl
index eb9be9d34aa9..012346ab1f28 100644
--- a/src/Serialization/polymake.jl
+++ b/src/Serialization/polymake.jl
@@ -95,6 +95,9 @@ _pmdata_for_oscar(v::Polymake.Vector{<:Polymake.Rational}, coeff::Field) = colle
 
 _pmdata_for_oscar(v::Polymake.SparseVector, coeff::Field) = _pmdata_for_oscar(Polymake.common.dense(v), coeff)
 
+_pmdata_for_oscar(nm::Polymake.NodeMap, coeff::Field) = _pmdata_for_oscar(Polymake.Array(nm), coeff)
+_pmdata_for_oscar(bd::Polymake.BasicDecoration, coeff::Field) = (_pmdata_for_oscar(Polymake.decoration_face(bd), coeff), _pmdata_for_oscar(Polymake.decoration_rank(bd), coeff))
+
 _pmdata_for_oscar(s::Polymake.Integer, coeff::Field) = ZZ(s)
 _pmdata_for_oscar(s::Polymake.Rational, coeff::Field) = QQ(s)
 _pmdata_for_oscar(s::Polymake.OscarNumber, coeff::Field) = coeff(s)
@@ -106,6 +109,8 @@ _pmdata_for_oscar(s::Polymake.TropicalNumber{A}, coeff::Field) where A = tropica
 _pmdata_for_oscar(s::Polymake.CxxWrap.StdString, coeff::Field) = String(s)
 
 _pmdata_for_oscar(a::Polymake.Array, coeff::Field) = [_pmdata_for_oscar(e, coeff) for e in a]
+_pmdata_for_oscar(a::Polymake.Array{T}, coeff::Field) where T <: Union{Polymake.Matrix, Polymake.Vector} = Tuple(_pmdata_for_oscar.(a, Ref(coeff)))
+
 _pmdata_for_oscar(s::Polymake.Set, coeff::Field) = Set(_pmdata_for_oscar(e, coeff) for e in s)
 
 
@@ -145,6 +150,7 @@ function _polyhedral_object_as_dict(x::Oscar.PolyhedralObjectUnion)
 end
 
 function _load_bigobject_from_dict!(obj::Polymake.BigObject, dict::Dict, parent_key::String="")
+  delay_loading = Tuple{String,Any}[]
   for (k, v) in dict
     key_str = parent_key == "" ? k : parent_key * "." * k
     first(k) == '_' && continue
@@ -152,9 +158,22 @@ function _load_bigobject_from_dict!(obj::Polymake.BigObject, dict::Dict, parent_
     if v isa Dict
       _load_bigobject_from_dict!(obj, v, key_str)
     else
-      Polymake.take(obj, key_str, convert(Polymake.PolymakeType, v))
+      pmv = convert(Polymake.PolymakeType, v)
+      bot = Polymake.bigobject_type(obj)
+      # NodeMaps need extra treatment since the constructor doesn't accept polymake c++ arrays
+      # and we can't create a nodemap from scratch without the graph
+      # so we convert it to a pure perl array and delay loading until the end of this level
+      if pmv isa Polymake.Array && Polymake.bigobject_prop_type(bot, key_str) in ["NodeMap", "EdgeMap"]
+        pmv = Polymake.as_perl_array_of_array(pmv)
+        push!(delay_loading, (key_str, pmv))
+      else
+        Polymake.take(obj, key_str, pmv)
+      end
     end
   end
+  for (k, v) in delay_loading
+    Polymake.take(obj, k, v)
+  end
   if haskey(dict, "_description")
     Polymake.setdescription!(obj, dict["_description"])
   end
diff --git a/test/Combinatorics/Graph.jl b/test/Combinatorics/Graph.jl
index 7259ba0716fc..0e6ef72156b8 100644
--- a/test/Combinatorics/Graph.jl
+++ b/test/Combinatorics/Graph.jl
@@ -160,6 +160,16 @@
         @test n_vertices(G2) == 13
         @test n_edges(G2) == 5
 
+        ei = edges(G2)
+        @test length(ei) == 5
+
+        ee = collect(ei)
+        @test length(ei) == 0
+        @test collect(ei) == Edge[]
+
+        GG2 = graph_from_edges(Undirected, ee, 13)
+        @test is_isomorphic(G2, GG2)
+
     end
 
     @testset "adjacency_matrix laplacian_matrix" begin
diff --git a/test/PolyhedralGeometry/polyhedron.jl b/test/PolyhedralGeometry/polyhedron.jl
index 9a44f26384f1..e5d742777787 100644
--- a/test/PolyhedralGeometry/polyhedron.jl
+++ b/test/PolyhedralGeometry/polyhedron.jl
@@ -46,7 +46,6 @@
     @test !([-1, -1] in Q0)
     @test n_vertices(Q0) == 3
     @test n_vertices.(faces(Q0, 1)) == [2, 2, 2]
-    if T == QQFieldElem
       @test lattice_points(Q0) isa SubObjectIterator{PointVector{ZZRingElem}}
       @test point_matrix(lattice_points(Q0)) == matrix(ZZ, [0 0; 0 1; 1 0])
       @test matrix(ZZ, lattice_points(Q0)) == matrix(ZZ, [0 0; 0 1; 1 0])
@@ -63,6 +62,7 @@
       @test length(boundary_lattice_points(square)) == 8
       @test boundary_lattice_points(square) ==
         [[-1, -1], [-1, 0], [-1, 1], [0, -1], [0, 1], [1, -1], [1, 0], [1, 1]]
+    if T == QQFieldElem
       @test is_smooth(Q0)
       @test is_normal(Q0)
       @test is_lattice_polytope(Q0)
diff --git a/test/PolyhedralGeometry/scalar_types.jl b/test/PolyhedralGeometry/scalar_types.jl
index 9bc361413fb6..a2c4c2cade1a 100644
--- a/test/PolyhedralGeometry/scalar_types.jl
+++ b/test/PolyhedralGeometry/scalar_types.jl
@@ -43,6 +43,9 @@
   @test _edge_length_for_test.(faces(sd, 1)) == repeat([4], 18)
   # scaling the Polyhedron by 3 yields edge lengths of 6
   @test _edge_length_for_test.(faces(3 * sd, 1)) == repeat([36], 18)
+  # there are 11 lattice points
+  @test length(lattice_points(sd)) == 11
+
   let pc = polyhedral_complex(
       E, IncidenceMatrix(facets(sd)), vertices(sd); non_redundant=true
     )
@@ -62,6 +65,8 @@
   @test number_of_vertices(qp) == 3
   @test number_of_facets(qp) == 3
 
+  @test length(lattice_points(qp)) == 1
+
   @testset "Scalar detection" begin
     let j = johnson_solid(12)
       @test j isa Polyhedron{QQFieldElem}
diff --git a/test/Serialization/PolyhedralGeometry.jl b/test/Serialization/PolyhedralGeometry.jl
index e75f5bee8dcf..6d16fd8f8b66 100644
--- a/test/Serialization/PolyhedralGeometry.jl
+++ b/test/Serialization/PolyhedralGeometry.jl
@@ -30,23 +30,30 @@ using Oscar: _integer_variables
 
     @testset "Polyhedron" begin
       square = cube(2)
+      f_vector(square)
       test_save_load_roundtrip(path, square) do loaded
         @test n_vertices(square) == n_vertices(loaded)
         @test dim(square) == dim(loaded)
         @test square == loaded
+        @test Polymake.exists(Oscar.pm_object(loaded), "HASSE_DIAGRAM.DECORATION")
       end
 
       n2 = (QQBarField()(5))^(QQ(4//5))
       c = cube(QQBarField(), 3, -1, n2)
-      test_save_load_roundtrip(path, square) do loaded
-        @test n_vertices(square) == n_vertices(loaded)
-        @test dim(square) == dim(loaded)
-        @test square == loaded
+      f_vector(c)
+      lattice_points(c)
+      test_save_load_roundtrip(path, c) do loaded
+        @test n_vertices(c) == n_vertices(loaded)
+        @test dim(c) == dim(loaded)
+        @test c == loaded
+        @test Polymake.exists(Oscar.pm_object(loaded), "HASSE_DIAGRAM.DECORATION")
       end
 
       d_hedron = dodecahedron()
       facets(d_hedron)
       vertices(d_hedron)
+      f_vector(d_hedron)
+      lattice_points(d_hedron)
 
       dict_ps = Dict{String, Any}(
         "unprecise" => polyhedron(