diff --git a/src/MultipleScattering.jl b/src/MultipleScattering.jl
index e845db00..0bb2de7a 100644
--- a/src/MultipleScattering.jl
+++ b/src/MultipleScattering.jl
@@ -3,7 +3,7 @@ __precompile__()
 module MultipleScattering
 
 ## Shapes
-export Shape, Circle, Rectangle, Box, EmptyShape, Halfspace, TimeOfFlight, TimeOfFlightFromPoint
+export Shape, Circle, Rectangle, Box, EmptyShape, Halfspace, Plate, TimeOfFlight, TimeOfFlightFromPoint
 
 export outer_radius, volume, name, iscongruent, (≅), congruent, in, issubset, origin, shape, Sphere, (==), isequal, show
 export boundary_functions, boundary_points, boundary_data, bounding_box, box_corners
diff --git a/src/physics/special_functions.jl b/src/physics/special_functions.jl
index 96a71e0d..029ef810 100644
--- a/src/physics/special_functions.jl
+++ b/src/physics/special_functions.jl
@@ -190,7 +190,7 @@ cartesian_to_radial_coordinates(x::Vector) = cartesian_to_radial_coordinates(SVe
 radial_to_cartesian_coordinates(θ::Vector) = radial_to_cartesian_coordinates(SVector(θ...))
 
 function cartesian_to_radial_coordinates(x::SVector{3,CT}) where CT
-    r = sqrt(sum(x .^2)) # note this should be complex if x is complex
+    r = sqrt(sum(x .^2)) # note this is, and should be, a complex number when x is a complex vector
     θ = atan(sqrt(x[1]^2+x[2]^2),x[3])
     φ = atan(x[2], x[1])
     return [r,θ,φ]
diff --git a/src/shapes/halfspace.jl b/src/shapes/halfspace.jl
index 7419ea88..bb8e96cd 100644
--- a/src/shapes/halfspace.jl
+++ b/src/shapes/halfspace.jl
@@ -1,7 +1,7 @@
 """
     Halfspace(normal::AbstractVector{T} [, origin::AbstractVector{T}=zeros()])
 
-N-dimensional [`Shape`](@ref) defined by all points x = origin - λ * normal, for any λ > 0.
+A halfspace defined by all the points ``\\mathbf x`` that satify ``(\\mathbf x - \\mathbf o) \\cdot \\mathbf n < 0`` where ``\\mathbf n`` is the unit normal and ``\\mathbf o`` is the origin.
 """
 struct Halfspace{T,Dim} <: Shape{T,Dim}
     normal::SVector{Dim,T} # outward pointing normal vector
diff --git a/src/shapes/plate.jl b/src/shapes/plate.jl
new file mode 100644
index 00000000..695fda93
--- /dev/null
+++ b/src/shapes/plate.jl
@@ -0,0 +1,69 @@
+"""
+    Plate(normal::AbstractVector{T}, width::T, [, origin::AbstractVector{T}=zeros()])
+
+A plate defined by all the points ``\\mathbf x`` that satify ``|(\\mathbf x - \\mathbf o) \\cdot \\mathbf n| < w /2`` where ``\\mathbf n`` is the unit normal, ``\\mathbf o`` is the origin, and ``w`` is the width.
+"""
+struct Plate{T,Dim} <: Shape{T,Dim}
+    normal::SVector{Dim,T} # outward pointing normal vector
+    width::T # the width
+    origin::SVector{Dim,T}
+end
+
+# Constructors
+Plate(normal::AbstractVector{T}, width::T, origin::AbstractVector{T} = zeros(T,length(normal))) where {T} = Plate{T,length(normal)}(normal ./ norm(normal), width, origin)
+
+Plate(normal::NTuple{Dim,T}, width::T, origin::AbstractVector{T} = zeros(T,Dim)) where {T,Dim} = Plate{T,Dim}(normal ./ norm(normal), width, origin)
+
+name(shape::Plate) = "Plate"
+
+volume(shape::Plate) = Inf
+outer_radius(hs::Plate{T}) where T = T(Inf)
+
+# import Base.issubset
+# function issubset(inner_rect::Plate{T}, outer_rect::Plate{T}) where T
+#     all(topright(inner_rect) .<= topright(outer_rect)) &&
+#     all(bottomleft(inner_rect) .>= bottomleft(outer_rect))
+# end
+
+import Base.in
+function in(x::AbstractVector{T}, p::Plate)::Bool where T
+    abs(dot(x - p.origin, p.normal)) < p.width / T(2)
+end
+
+import Base.(==)
+function ==(h1::Plate{T}, h2::Plate{T}) where T
+    h1.origin == h2.origin &&
+    h1.width == h2.width &&
+    h1.normal == h2.normal
+end
+
+import Base.isequal
+function isequal(h1::Plate{T}, h2::Plate{T}) where T
+    isequal(h1.origin, h2.origin) &&
+    isequal(h1.width, h2.width) &&
+    isequal(h1.normal, h2.normal)
+end
+
+function iscongruent(h1::Plate{T}, h2::Plate{T}) where T
+    (h1.normal  == h2.normal) && (h1.width  == h2.width)
+end
+
+function congruent(h::Plate{T}, x) where T
+    Plate(h.normal, h.width, x)
+end
+
+# function boundary_functions(h::Plate{T,2}, scale::T = 10.0) where T
+#     surface_vec = [-h.normal[2], h.normal[1]]
+#
+#     function x(t)
+#         check_boundary_coord_range(t)
+#         h.origin[1] + surface_vec[1] * width/2 + t * scale * surface_vec[1]
+#     end
+#
+#     function y(t)
+#         check_boundary_coord_range(t)
+#         h.origin[2] + t * scale * surface_vec[2]
+#     end
+#
+#     return x, y
+# end
diff --git a/src/shapes/rectangle.jl b/src/shapes/rectangle.jl
deleted file mode 100644
index d9134e5a..00000000
--- a/src/shapes/rectangle.jl
+++ /dev/null
@@ -1,100 +0,0 @@
-"""
-    Rectangle([origin::AbstractVector{T}=zeros(),] width::T, Height::T)
-    Rectangle(bottomleft::AbstractVector{T}, topright::AbstractVector{T})
-
-2D [`Shape`](@ref) with axis aligned sides, defined by width, height and origin (at the center).
-"""
-struct Rectangle{T} <: Shape{T,2}
-    origin::SVector{2,T}
-    width::T
-    height::T
-end
-
-# Alternative constructor, where bottomleft and topright corners are specified
-function Rectangle(bottomleft::Union{AbstractVector{T},NTuple{2,T}}, topright::Union{AbstractVector{T},NTuple{2,T}}) where {T}
-    origin = (bottomleft .+ topright)./2
-    width = topright[1] - bottomleft[1]
-    height = topright[2] - bottomleft[2]
-    if sum(bottomleft .< topright) < 2
-        error("bottomleft: $bottomleft should be below and left of topright: $topright.")
-    end
-    Rectangle{T}(origin, width, height)
-end
-
-# Alternate constructors, where type is inferred naturally
-Rectangle(origin::Tuple{T,T}, width::T, height::T) where {T} = Rectangle{T}(origin, width, height)
-Rectangle(origin::Vector{T}, width::T, height::T) where {T} = Rectangle{T}(origin, width, height)
-# If no position is given, assume origin is at zero
-Rectangle(width::T, height::T) where {T} = Rectangle{T}(SVector(zero(T),zero(T)), width, height)
-
-name(shape::Rectangle) = "Rectangle"
-
-outer_radius(r::Rectangle) = sqrt((r.width/2)^2 + (r.height/2)^2)
-volume(rectangle::Rectangle) = rectangle.width*rectangle.height
-
-import Base.issubset
-function issubset(inner_rect::Rectangle{T}, outer_rect::Rectangle{T}) where T
-    all(topright(inner_rect) .<= topright(outer_rect)) &&
-    all(bottomleft(inner_rect) .>= bottomleft(outer_rect))
-end
-
-import Base.in
-function in(x::AbstractVector, r::Rectangle)::Bool
-    all(abs.(x .- r.origin) .<= SVector(r.width, r.height))
-end
-
-import Base.(==)
-function ==(r1::Rectangle{T}, r2::Rectangle{T}) where T
-    r1.origin == r2.origin &&
-    r1.width  == r2.width  &&
-    r1.height == r2.height
-end
-
-import Base.isequal
-function isequal(r1::Rectangle{T}, r2::Rectangle{T}) where T
-    isequal(r1.origin, r2.origin) &&
-    isequal(r1.width , r2.width ) &&
-    isequal(r1.height, r2.height)
-end
-
-function iscongruent(r1::Rectangle{T}, r2::Rectangle{T}) where T
-    r1.width  == r2.width  &&
-    r1.height == r2.height
-end
-
-function congruent(r::Rectangle{T}, x) where T
-    Rectangle{T}(x, r.width, r.height)
-end
-
-# Rectangle bounds itself
-bounding_box(rect::Rectangle) = rect
-
-"Return SVector with the coordinates of the bottom left of a rectangle"
-bottomleft(rect::Rectangle) = origin(rect) .- SVector(rect.width/2, rect.height/2)
-
-"Return SVector with the coordinates of the top right of a rectangle"
-topright(rect::Rectangle)   = origin(rect) .+ SVector(rect.width/2, rect.height/2)
-
-
-function boundary_functions(rect::Rectangle)
-
-    function x(t)
-        check_boundary_coord_range(t)
-        if     t <= 1//4 x = bottomleft(rect)[1] + 4t*rect.width
-        elseif t <= 2//4 x = topright(rect)[1]
-        elseif t <= 3//4 x = topright(rect)[1] - 4*(t-2//4)*rect.width
-        else             x = bottomleft(rect)[1]
-        end
-    end
-
-    function y(t)
-        check_boundary_coord_range(t)
-        if     t <= 1//4 x = bottomleft(rect)[2]
-        elseif t <= 2//4 x = bottomleft(rect)[2] + 4*(t-1//4)*rect.height
-        elseif t <= 3//4 x = topright(rect)[2]
-        else             x = topright(rect)[2] - 4*(t-3//4)*rect.height
-        end
-    end
-
-    return x, y
-end
diff --git a/src/shapes/shapes.jl b/src/shapes/shapes.jl
index b932beea..da1074e3 100644
--- a/src/shapes/shapes.jl
+++ b/src/shapes/shapes.jl
@@ -41,9 +41,11 @@ end
 include("box.jl")
 include("sphere.jl")
 include("halfspace.jl")
+include("plate.jl")
 include("time_of_flight.jl")
 include("time_of_flight_from_point.jl")
 include("empty_shape.jl")
+
 """
     points_in_shape(Shape; res = 20, xres = res, yres = res,
              exclude_region = EmptyShape(region), kws...)
diff --git a/test/shapetests.jl b/test/shapetests.jl
index 6d6cfd03..4f492e1a 100644
--- a/test/shapetests.jl
+++ b/test/shapetests.jl
@@ -142,4 +142,20 @@
 
         @test true
     end
+
+    @testset "Infinite volume shapes" begin
+        normal = rand(3);
+        origin = rand(3);
+        width = 1.0 + rand();
+        p = Plate(normal, width, origin)
+        h = Halfspace(normal, origin)
+
+        shapes = [p,h];
+
+        @test isempty(findall( (volume.(shapes) .== Inf) .== 0))
+
+        xs = [rand(3) for i = 1:10];
+        [[x ∈ s for x in xs] for s in shapes]
+
+    end
 end