diff --git a/src/PolyhedralGeometry/helpers.jl b/src/PolyhedralGeometry/helpers.jl
index 061e45191959..1bfc934c9286 100644
--- a/src/PolyhedralGeometry/helpers.jl
+++ b/src/PolyhedralGeometry/helpers.jl
@@ -75,12 +75,15 @@ Set{Int64} with 1 element:
 """
 column(i::IncidenceMatrix, n::Int) = convert(Set{Int}, Polymake.col(i, n))
 
+const _polymake_scalars = Union{Polymake.Integer, Polymake.Rational, Polymake.QuadraticExtension, Polymake.OscarNumber, Float64, Polymake.TropicalNumber}
+const _polymake_compatible_scalars = Union{QQFieldElem, ZZRingElem, Base.Integer, Base.Rational, _polymake_scalars}
+
 function assure_matrix_polymake(m::Union{AbstractMatrix{Any}, AbstractMatrix{FieldElem}})
     a, b = size(m)
     if a > 0
         i = findfirst(_cannot_convert_to_fmpq, m)
         t = i === nothing ? QQFieldElem : typeof(m[i])
-        if t <: Union{Polymake.Rational, Polymake.QuadraticExtension{Polymake.Rational}, Polymake.OscarNumber, Float64}
+        if t <: _polymake_scalars
             m = Polymake.Matrix{Polymake.convert_to_pm_type(t)}(m)
         else
             m = Polymake.Matrix{_scalar_type_to_polymake(t)}(m)
@@ -95,9 +98,9 @@ assure_matrix_polymake(m::AbstractMatrix{<:FieldElem}) = Polymake.Matrix{Polymak
 
 assure_matrix_polymake(m::MatElem) = Polymake.Matrix{_scalar_type_to_polymake(eltype(m))}(m)
 
-assure_matrix_polymake(m::Union{Oscar.ZZMatrix, Oscar.QQMatrix, AbstractMatrix{<:Union{QQFieldElem, ZZRingElem, Base.Integer, Base.Rational, Polymake.Rational, Polymake.QuadraticExtension, Polymake.OscarNumber, Float64}}}) = m
+assure_matrix_polymake(m::Union{Oscar.ZZMatrix, Oscar.QQMatrix, AbstractMatrix{<:_polymake_compatible_scalars}}) = m
 
-assure_matrix_polymake(m::SubArray{T, 2, U, V, W}) where {T<:Union{Polymake.Rational, Polymake.QuadraticExtension, Float64}, U, V, W} = Polymake.Matrix{T}(m)
+assure_matrix_polymake(m::SubArray{T, 2, U, V, W}) where {T<:Union{_polymake_scalars}, U, V, W} = Polymake.Matrix{T}(m)
 
 function assure_vector_polymake(v::Union{AbstractVector{Any}, AbstractVector{FieldElem}})
     i = findfirst(_cannot_convert_to_fmpq, v)
@@ -107,7 +110,7 @@ end
 
 assure_vector_polymake(v::AbstractVector{<:FieldElem}) = Polymake.Vector{Polymake.OscarNumber}(v)
 
-assure_vector_polymake(v::AbstractVector{<:Union{QQFieldElem, ZZRingElem, Base.Integer, Base.Rational, Polymake.Rational, Polymake.QuadraticExtension, Polymake.OscarNumber, Float64}}) = v
+assure_vector_polymake(v::AbstractVector{<:_polymake_compatible_scalars}) = v
 
 affine_matrix_for_polymake(x::Tuple{<:AnyVecOrMat, <:AbstractVector}) = augment(unhomogenized_matrix(x[1]), -Vector(assure_vector_polymake(x[2])))
 affine_matrix_for_polymake(x::Tuple{<:AnyVecOrMat, <:Any}) = homogenized_matrix(x[1], -x[2])
@@ -125,7 +128,7 @@ number_of_rows(x::SubArray{T, 2, U, V, W}) where {T, U, V, W} = size(x, 1)
 _isempty_halfspace(x::Pair{<:Union{Oscar.MatElem, AbstractMatrix}, Any}) = isempty(x[1])
 _isempty_halfspace(x) = isempty(x)
 
-function Polymake.Matrix{T}(x::Union{MatElem,AbstractMatrix{<:FieldElem}}) where T<:Union{Float64, Polymake.Rational, Polymake.Integer, Polymake.OscarNumber}
+function Polymake.Matrix{T}(x::Union{MatElem,AbstractMatrix{<:FieldElem}}) where T<:_polymake_scalars
     res = Polymake.Matrix{T}(size(x)...)
     return res .= x
 end
@@ -188,14 +191,16 @@ end
 (F::Field)(x::Polymake.Rational) = F(QQ(x))
 (F::Field)(x::Polymake.OscarNumber) = F(Polymake.unwrap(x))
 
+Polymake.convert_to_pm_type(::Type{typeof(min)}) = Polymake.Min
+Polymake.convert_to_pm_type(::Type{typeof(max)}) = Polymake.Max
+
 Polymake.convert_to_pm_type(::Type{ZZMatrix}) = Polymake.Matrix{Polymake.Integer}
 Polymake.convert_to_pm_type(::Type{QQMatrix}) = Polymake.Matrix{Polymake.Rational}
 Polymake.convert_to_pm_type(::Type{ZZRingElem}) = Polymake.Integer
 Polymake.convert_to_pm_type(::Type{QQFieldElem}) = Polymake.Rational
 Polymake.convert_to_pm_type(::Type{T}) where T<:FieldElem = Polymake.OscarNumber
-Polymake.convert_to_pm_type(::Type{<:Oscar.MatElem}) = Polymake.Matrix{Polymake.OscarNumber}
+Polymake.convert_to_pm_type(::Type{<:MatElem{T}}) where T = Polymake.Matrix{Polymake.convert_to_pm_type(T)}
 Polymake.convert_to_pm_type(::Type{<:Graph{T}}) where T<:Union{Directed,Undirected} = Polymake.Graph{T}
-Polymake.convert_to_pm_type(::Type{<:MatElem{Float64}}) = Polymake.Matrix{Float64}
 
 Base.convert(::Type{<:Polymake.Graph{T}}, g::Graph{T}) where T<:Union{Directed,Undirected} = Oscar.pm_object(g)
 
diff --git a/src/Serialization/polymake.jl b/src/Serialization/polymake.jl
index 4b876581d5e3..1ba57c2aa897 100644
--- a/src/Serialization/polymake.jl
+++ b/src/Serialization/polymake.jl
@@ -97,6 +97,10 @@ _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)
 
+_convert_pm_minormax(::Type{Polymake.Max}) = typeof(max)
+_convert_pm_minormax(::Type{Polymake.Min}) = typeof(min)
+_pmdata_for_oscar(s::Polymake.TropicalNumber{A}, coeff::Field) where A = tropical_semiring(_convert_pm_minormax(A))(s)
+
 _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]
diff --git a/src/TropicalGeometry/hypersurface.jl b/src/TropicalGeometry/hypersurface.jl
index d7ca5a50d099..091b9f44002a 100644
--- a/src/TropicalGeometry/hypersurface.jl
+++ b/src/TropicalGeometry/hypersurface.jl
@@ -51,30 +51,11 @@ function tropical_hypersurface(TropV::TropicalVarietySupertype{minOrMax,true}) w
     return tropical_hypersurface(polyhedral_complex(TropV),multiplicities(TropV),convention(TropV))
 end
 
-# Decompose a tropical polynomial into parts that Polymake can eat.
-# First function deals with the coefficients,
-# Second function then deals with the entire polynomial.
-function homogenize_and_convert_to_pm(t::TropicalSemiringElem{minOrMax}) where {minOrMax<:Union{typeof(max), typeof(min)}}
-   Add = (minOrMax==typeof(max)) ? Polymake.Max : Polymake.Min
-   if isinf(t)
-      return Polymake.TropicalNumber{Add}()
-   else
-      return Polymake.TropicalNumber{Add}(Polymake.new_rational_from_fmpq(data(t)))
-   end
-end
-
+# Decompose and homogenize a tropical polynomial into parts that Polymake can eat.
 function homogenize_and_convert_to_pm(f::Oscar.MPolyRingElem{TropicalSemiringElem{minOrMax}}) where {minOrMax<:Union{typeof(max), typeof(min)}}
-   Add = (minOrMax==typeof(max)) ? Polymake.Max : Polymake.Min
-   coeffs = Polymake.TropicalNumber{Add}[]
    td = total_degree(f)
-   exps = Vector{Int}[]
-   for (c,alpha) in zip(coefficients(f),exponents(f))
-      push!(coeffs, homogenize_and_convert_to_pm(c))
-      prepend!(alpha, td-sum(alpha))
-      push!(exps, alpha)
-   end
-   exps = matrix(ZZ, exps)
-   coeffs = Polymake.Vector{Polymake.TropicalNumber{Add, Polymake.Rational}}(coeffs)
+   exps = matrix(ZZ, collect([td-sum(alpha); alpha] for alpha in exponents(f)))
+   coeffs = collect(coefficients(f))
    return coeffs, exps
 end
 
@@ -175,9 +156,8 @@ julia> # tropical_hypersurface(Delta) # issue 2628
 function tropical_hypersurface(Delta::SubdivisionOfPoints, minOrMax::Union{typeof(min),typeof(max)}=min;
                                weighted_polyhedral_complex_only::Bool=false)
 
-    PMinOrMax =  (minOrMax==typeof(min)) ? Polymake.Min : Polymake.Max
-    coeffs = Polymake.TropicalNumber{PMinOrMax}.(Polymake.new_integer_from_fmpz.(min_weights(Delta)))
-    exps = ZZ.(matrix(QQ,points(Delta)))
+    coeffs = min_weights(Delta)
+    exps = points(Delta)
     pmhypproj = Polymake.tropical.Hypersurface{minOrMax}(MONOMIALS=exps, COEFFICIENTS=coeffs)
     pmhyp = Polymake.tropical.affine_chart(pmhypproj)
 
diff --git a/src/TropicalGeometry/semiring.jl b/src/TropicalGeometry/semiring.jl
index 277a0aa3e99f..bda0454c1db5 100644
--- a/src/TropicalGeometry/semiring.jl
+++ b/src/TropicalGeometry/semiring.jl
@@ -408,3 +408,22 @@ end
 
 Oscar.mul!(x::TropicalSemiringElem, y::TropicalSemiringElem, z::TropicalSemiringElem) = y * z
 Oscar.addeq!(y::TropicalSemiringElem, z::TropicalSemiringElem) = y + z
+
+
+################################################################################
+#
+#  helpers for polymake conversion
+#
+################################################################################
+
+Polymake.convert_to_pm_type(::Type{<:TropicalSemiringElem{A}}) where A = Polymake.TropicalNumber{Polymake.convert_to_pm_type(A),Polymake.Rational}
+
+function Base.convert(::Type{<:Polymake.TropicalNumber{PA}}, t::TropicalSemiringElem{A}) where {A <: Union{typeof(min),typeof(max)}, PA <: Union{Polymake.Min, Polymake.Max}}
+  @req PA == Polymake.convert_to_pm_type(A) "cannot convert between different tropical conventions"
+  isinf(t) ? Polymake.TropicalNumber{PA}() : Polymake.TropicalNumber{PA}(convert(Polymake.Rational, data(t)))
+end
+
+function (T::TropicalSemiring{A})(t::Polymake.TropicalNumber{PA}) where {A <: Union{typeof(min),typeof(max)}, PA <: Union{Polymake.Min, Polymake.Max}}
+  @req PA == Polymake.convert_to_pm_type(A) "cannot convert between different tropical conventions"
+  t == Polymake.zero(t) ? zero(T) : T(Polymake.scalar(t))
+end