diff --git a/Project.toml b/Project.toml
index f2bd7daec..133ffb0ed 100644
--- a/Project.toml
+++ b/Project.toml
@@ -26,7 +26,7 @@ GenericLinearAlgebra = "0.3"
 IterativeSolvers = "0.9"
 LinearMaps = "3"
 LowRankOpt = "0.2"
-MathOptInterface = "1"
+MathOptInterface = "1.20"
 PolynomialRoots = "1"
 Requires = "1"
 SpecialFunctions = "2"
diff --git a/examples/JuMP_utils.jl b/examples/JuMP_utils.jl
index 7be32ad4d..5ab7c643c 100644
--- a/examples/JuMP_utils.jl
+++ b/examples/JuMP_utils.jl
@@ -25,7 +25,7 @@ MOIU.@model(
         MOI.SecondOrderCone,
         MOI.RotatedSecondOrderCone,
         MOI.ExponentialCone,
-        MOI.PositiveSemidefiniteConeTriangle,
+        MOI.Scaled{MOI.PositiveSemidefiniteConeTriangle},
     ),
     (),
     (),
@@ -45,7 +45,7 @@ MOIU.@model(
         MOI.Nonnegatives,
         MOI.Nonpositives,
         MOI.ExponentialCone,
-        MOI.PositiveSemidefiniteConeTriangle,
+        MOI.Scaled{MOI.PositiveSemidefiniteConeTriangle},
     ),
     (),
     (),
diff --git a/src/MathOptInterface/cones.jl b/src/MathOptInterface/cones.jl
index 8afa862a1..572ccf434 100644
--- a/src/MathOptInterface/cones.jl
+++ b/src/MathOptInterface/cones.jl
@@ -22,7 +22,7 @@ end
 
 function cone_from_moi(
     ::Type{T},
-    cone::MOI.PositiveSemidefiniteConeTriangle,
+    cone::MOI.Scaled{MOI.PositiveSemidefiniteConeTriangle},
 ) where {T <: Real}
     return Cones.PosSemidefTri{T, T}(MOI.dimension(cone))
 end
@@ -77,7 +77,10 @@ function cone_from_moi(::Type{T}, cone::MOI.GeometricMeanCone) where {T <: Real}
     return (l = MOI.dimension(cone) - 1; Cones.HypoGeoMean{T}(1 + l))
 end
 
-function cone_from_moi(::Type{T}, cone::MOI.RootDetConeTriangle) where {T <: Real}
+function cone_from_moi(
+    ::Type{T},
+    cone::MOI.Scaled{MOI.RootDetConeTriangle},
+) where {T <: Real}
     return Cones.HypoRootdetTri{T, T}(MOI.dimension(cone))
 end
 
@@ -89,7 +92,10 @@ function cone_from_moi(::Type{T}, cone::MOI.DualExponentialCone) where {T <: Rea
     return Cones.HypoPerLog{T}(3, use_dual = true)
 end
 
-function cone_from_moi(::Type{T}, cone::MOI.LogDetConeTriangle) where {T <: Real}
+function cone_from_moi(
+    ::Type{T},
+    cone::MOI.Scaled{MOI.LogDetConeTriangle},
+) where {T <: Real}
     return Cones.HypoPerLogdetTri{T, T}(MOI.dimension(cone))
 end
 
@@ -795,7 +801,7 @@ const HypatiaCones{T <: Real} = Union{
 const SupportedCone{T <: Real} = Union{
     HypatiaCones{T},
     MOI.Nonnegatives,
-    MOI.PositiveSemidefiniteConeTriangle,
+    MOI.Scaled{MOI.PositiveSemidefiniteConeTriangle},
     MOI.HermitianPositiveSemidefiniteConeTriangle,
     MOI.NormInfinityCone,
     MOI.NormOneCone,
@@ -806,10 +812,10 @@ const SupportedCone{T <: Real} = Union{
     MOI.PowerCone{T},
     MOI.DualPowerCone{T},
     MOI.GeometricMeanCone,
-    MOI.RootDetConeTriangle,
+    MOI.Scaled{MOI.RootDetConeTriangle},
     MOI.ExponentialCone,
     MOI.DualExponentialCone,
-    MOI.LogDetConeTriangle,
+    MOI.Scaled{MOI.LogDetConeTriangle},
     MOI.RelativeEntropyCone,
     _PrimalRankOnePSD{T},
     _DualRankOnePSD{T},
diff --git a/src/MathOptInterface/transform.jl b/src/MathOptInterface/transform.jl
index d8e6b98c9..002b58313 100644
--- a/src/MathOptInterface/transform.jl
+++ b/src/MathOptInterface/transform.jl
@@ -48,46 +48,6 @@ function permute_affine(cone::SpecNucCone, func::VAF{T}) where {T}
     return idxs_new
 end
 
-# transformations (svec rescaling) for MOI symmetric matrix cones not
-# in svec (scaled lower triangle) form
-const SvecCone = Union{
-    MOI.PositiveSemidefiniteConeTriangle,
-    MOI.LogDetConeTriangle,
-    MOI.RootDetConeTriangle,
-}
-
-svec_offset(::MOI.PositiveSemidefiniteConeTriangle) = 1
-svec_offset(::MOI.RootDetConeTriangle) = 2
-svec_offset(::MOI.LogDetConeTriangle) = 3
-
-needs_untransform(::SvecCone) = true
-
-function untransform_affine(cone::SvecCone, vals::AbstractVector{T}) where {T}
-    @views svec_vals = vals[svec_offset(cone):end]
-    Cones.scale_svec!(svec_vals, inv(sqrt(T(2))))
-    return vals
-end
-
-needs_rescale(::SvecCone) = true
-
-function rescale_affine(cone::SvecCone, vals::AbstractVector{T}) where {T}
-    @views svec_vals = vals[svec_offset(cone):end]
-    Cones.scale_svec!(svec_vals, sqrt(T(2)))
-    return vals
-end
-
-function rescale_affine(cone::SvecCone, func::VAF{T}, vals::AbstractVector{T}) where {T}
-    scal_start = svec_offset(cone) - 1
-    rt2 = sqrt(T(2))
-    for i in eachindex(vals)
-        k = func.terms[i].output_index - scal_start
-        if k > 0 && !MOI.Utilities.is_diagonal_vectorized_index(k)
-            vals[i] *= rt2
-        end
-    end
-    return vals
-end
-
 # transformation (svec rescaling and real/imag parts reordering) for MOI Hermitian PSD cone not in svec (scaled upper triangle) form
 needs_untransform(::MOI.HermitianPositiveSemidefiniteConeTriangle) = true
 
diff --git a/test/moicones.jl b/test/moicones.jl
index 9815081c5..7d8d255b9 100644
--- a/test/moicones.jl
+++ b/test/moicones.jl
@@ -22,7 +22,7 @@ function test_moi_cones(T::Type{<:Real})
     # MOI predefined cones
 
     @testset "PositiveSemidefiniteConeTriangle" begin
-        moi_cone = MOI.PositiveSemidefiniteConeTriangle(3)
+        moi_cone = MOI.Scaled(MOI.PositiveSemidefiniteConeTriangle(3))
         hyp_cone = Hypatia.cone_from_moi(T, moi_cone)
         @test hyp_cone isa Cones.PosSemidefTri{T, T}
         @test MOI.dimension(moi_cone) == Cones.dimension(hyp_cone) == 6
@@ -114,7 +114,7 @@ function test_moi_cones(T::Type{<:Real})
     end
 
     @testset "RootDetConeTriangle" begin
-        moi_cone = MOI.RootDetConeTriangle(3)
+        moi_cone = MOI.Scaled(MOI.RootDetConeTriangle(3))
         hyp_cone = Hypatia.cone_from_moi(T, moi_cone)
         @test hyp_cone isa Cones.HypoRootdetTri{T, T}
         @test MOI.dimension(moi_cone) == Cones.dimension(hyp_cone) == 7
@@ -138,7 +138,7 @@ function test_moi_cones(T::Type{<:Real})
     end
 
     @testset "LogDetConeTriangle" begin
-        moi_cone = MOI.LogDetConeTriangle(3)
+        moi_cone = MOI.Scaled(MOI.LogDetConeTriangle(3))
         hyp_cone = Hypatia.cone_from_moi(T, moi_cone)
         @test hyp_cone isa Cones.HypoPerLogdetTri{T, T}
         @test MOI.dimension(moi_cone) == Cones.dimension(hyp_cone) == 8