diff --git a/Project.toml b/Project.toml
index e4be775..1fd3f9f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -31,9 +31,10 @@ julia = "1.6"
 
 [extras]
 Mendeleev = "c116f080-063d-490a-9873-2b5b2cce4c34"
+SymPy = "24249f21-da20-56a4-8eb1-6a02cf4ae2e6"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 UnitfulAtomic = "a7773ee8-282e-5fa2-be4e-bd808c38a91a"
 
 [targets]
-test = ["Mendeleev", "Test", "Unitful", "UnitfulAtomic"]
+test = ["Mendeleev", "SymPy", "Test", "Unitful", "UnitfulAtomic"]
diff --git a/src/metric.jl b/src/metric.jl
index 073aa40..af7f124 100644
--- a/src/metric.jl
+++ b/src/metric.jl
@@ -1,4 +1,4 @@
-using StaticArrays: SHermitianCompact
+using StaticArrays: SHermitianCompact, SDiagonal
 
 export MetricTensor, distance
 
@@ -11,10 +11,8 @@ MetricTensor(data::AbstractMatrix) = MetricTensor(SHermitianCompact{3}(data))
 
 Generate a `MetricTensor` from the three basis vectors.
 """
-function MetricTensor(𝐚::AbstractVector, 𝐛::AbstractVector, 𝐜::AbstractVector)
-    𝐚𝐛𝐜 = (𝐚, 𝐛, 𝐜)
-    return MetricTensor([dot(𝐱, 𝐲) for 𝐱 in 𝐚𝐛𝐜, 𝐲 in 𝐚𝐛𝐜])
-end
+MetricTensor(𝐚::AbstractVector, 𝐛::AbstractVector, 𝐜::AbstractVector) =
+    MetricTensor([dot(𝐱, 𝐲) for 𝐱 in (𝐚, 𝐛, 𝐜), 𝐲 in (𝐚, 𝐛, 𝐜)])
 """
     MetricTensor(lattice::Lattice)
 
@@ -51,7 +49,7 @@ distance(𝐚::AbstractVector, g::MetricTensor, 𝐛::AbstractVector) = g(𝐚,
 
 Construct a `Lattice` from a `MetricTensor`.
 """
-Lattice(g::MetricTensor) = Lattice(latticeconstants(g))
+Lattice(g::MetricTensor) = Lattice(latticeconstants(g)...)
 
 """
     latticeconstants(g::MetricTensor)
@@ -65,6 +63,20 @@ function latticeconstants(g::MetricTensor)
     return a, b, c, α, β, γ
 end
 
+# See https://github.com/JuliaLang/julia/blob/v1.10.0-beta1/stdlib/LinearAlgebra/src/uniformscaling.jl#L130-L131
+Base.one(::Type{MetricTensor{T}}) where {T} =
+    MetricTensor(SDiagonal(one(T), one(T), one(T)))
+Base.one(g::MetricTensor) = one(typeof(g))
+
+# See https://github.com/JuliaLang/julia/blob/v1.10.0-beta1/stdlib/LinearAlgebra/src/uniformscaling.jl#L132-L133
+Base.oneunit(::Type{MetricTensor{T}}) where {T} =
+    MetricTensor(SDiagonal(oneunit(T), oneunit(T), oneunit(T)))
+Base.oneunit(g::MetricTensor) = oneunit(typeof(g))
+
+# See https://github.com/JuliaLang/julia/blob/v1.10.0-beta1/stdlib/LinearAlgebra/src/uniformscaling.jl#L134-L135
+Base.zero(::Type{MetricTensor{T}}) where {T} = MetricTensor(zeros(T, 3, 3))
+Base.zero(lattice::MetricTensor) = zero(typeof(lattice))
+
 Base.parent(g::MetricTensor) = g.data
 
 Base.size(::MetricTensor) = (3, 3)
diff --git a/src/volume.jl b/src/volume.jl
index 29bbb22..0fc521c 100644
--- a/src/volume.jl
+++ b/src/volume.jl
@@ -20,7 +20,7 @@ cellvolume(cell::Cell) = cellvolume(Lattice(cell))
 
 Calculate the cell volume from a `MetricTensor`.
 """
-cellvolume(g::MetricTensor) = sqrt(_det(g.data))  # `sqrt` is always positive!
+cellvolume(g::MetricTensor) = sqrt(_det(parent(g)))  # `sqrt` is always positive!
 
 """
     crystaldensity(lattice::Lattice, atoms)
diff --git a/test/metric.jl b/test/metric.jl
index b8fe7c1..a24cc16 100644
--- a/test/metric.jl
+++ b/test/metric.jl
@@ -1,5 +1,23 @@
 using LinearAlgebra: dot, norm, diagm
-# using SymPy: symbols
+using SymPy: symbols
+
+@testset "Test consistency of constructors of `MetricTensor`" begin
+    lattice = Lattice(
+        4.59983732u"angstrom", 4.59983732u"angstrom", 2.95921356u"angstrom", 90, 90, 90
+    )
+    𝐚, 𝐛, 𝐜 = basisvectors(lattice)
+    @test MetricTensor(lattice) ==
+        MetricTensor(𝐚, 𝐛, 𝐜) ==
+        MetricTensor(
+            4.59983732u"angstrom", 4.59983732u"angstrom", 2.95921356u"angstrom", 90, 90, 90
+        )
+    @test Lattice(MetricTensor(lattice)) == lattice
+    @testset "Test `zero`, `one`, and `oneunit`" begin
+        @test one(MetricTensor(lattice)) == MetricTensor(one(lattice))
+        @test oneunit(MetricTensor(lattice)) == MetricTensor(oneunit(lattice))
+        @test zero(MetricTensor(lattice)) == MetricTensor(zero(lattice))
+    end
+end
 
 @testset "Test lengths in a hexagonal lattice" begin
     g = MetricTensor(1, 1, 2, 90, 90, 120)  # Primitive hexagonal
@@ -21,8 +39,8 @@ end
     @test distance(a, g, b)^2 == 13 / 9
 end
 
-# @testset "Symbolic calculation" begin
-#     a, c = symbols("a, c", positive = true)
-#     @test MetricTensor(a, a, c, 90, 90, 120) ==
-#           MetricTensor([a^2 -0.5*a^2 0; -0.5*a^2 a^2 0; 0 0 c^2])  # Primitive hexagonal
-# end
+@testset "Test symbolic calculation" begin
+    a, c = symbols("a, c"; positive=true)
+    @test MetricTensor(a, a, c, 90, 90, 120) ==
+        MetricTensor([a^2 -0.5*a^2 0; -0.5*a^2 a^2 0; 0 0 c^2])  # Primitive hexagonal
+end