diff --git a/CHANGELOG.md b/CHANGELOG.md
index 63cf5738691..751c686d034 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,7 +1,7 @@
 # Changelog
 
 ## [Unreleased]
-
+- Fix an error in `convert_arguments` for PointBased plots and 3D polygons [#4585](https://github.com/MakieOrg/Makie.jl/pull/4585).
 - Fix polygon rendering issue of `crossbar(..., show_notch = true)` in CairoMakie [#4587](https://github.com/MakieOrg/Makie.jl/pull/4587).
 
 ## [0.21.16] - 2024-11-06
diff --git a/src/conversions.jl b/src/conversions.jl
index cfdd000a1ae..b7412d8340f 100644
--- a/src/conversions.jl
+++ b/src/conversions.jl
@@ -261,7 +261,7 @@ function convert_arguments(PB::PointBased, mp::Union{Array{<:Polygon{N, T}}, Mul
         converted = convert_arguments(PB, mp[idx])[1] # this should always be a Tuple{<: Vector{Point}}
         append!(arr, converted)
         if idx != n # don't add NaN at the end
-            push!(arr, Point2(NaN))
+            push!(arr, Point{N, float_type(T)}(NaN))
         end
     end
     return (arr,)
diff --git a/test/convert_arguments.jl b/test/convert_arguments.jl
index a075c27b133..70d2885aca6 100644
--- a/test/convert_arguments.jl
+++ b/test/convert_arguments.jl
@@ -132,6 +132,7 @@ Makie.convert_arguments(::PointBased, ::MyConvVector) = ([Point(10, 20)],)
                 geom = Sphere(Point3{T_in}(0), T_in(1))
                 _mesh = GeometryBasics.mesh(rect3; pointtype=Point3{T_in}, facetype=GLTriangleFace)
                 polygon = Polygon(Point2.(xs, ys))
+                polygon3d = Polygon(Point3.(xs, ys, zs))
                 line = LineString(Point3.(xs, ys, zs))
                 bp = BezierPath([
                     MoveTo(T_in(0), T_in(0)),
@@ -228,6 +229,9 @@ Makie.convert_arguments(::PointBased, ::MyConvVector) = ([Point(10, 20)],)
                         @test apply_conversion(CT, polygon)    isa Tuple{Vector{Point2{T_out}}}
                         @test apply_conversion(CT, [polygon, polygon]) isa Tuple{Vector{Point2{T_out}}}
                         @test apply_conversion(CT, MultiPolygon([polygon, polygon])) isa Tuple{Vector{Point2{T_out}}}
+                        @test apply_conversion(CT, polygon3d)    isa Tuple{Vector{Point3{T_out}}}
+                        @test apply_conversion(CT, [polygon3d, polygon3d]) isa Tuple{Vector{Point3{T_out}}}
+                        @test apply_conversion(CT, MultiPolygon([polygon3d, polygon3d])) isa Tuple{Vector{Point3{T_out}}}
                         @test apply_conversion(CT, line)       isa Tuple{Vector{Point3{T_out}}}
                         @test apply_conversion(CT, [line, line]) isa Tuple{Vector{Point3{T_out}}}
                         @test apply_conversion(CT, MultiLineString([line, line])) isa Tuple{Vector{Point3{T_out}}}