From 12724ca7faf3e3f0bb43cffeea77970e4d3b5977 Mon Sep 17 00:00:00 2001
From: Yue Ren <yue.ren.kl@gmail.com>
Date: Sat, 11 Jan 2025 08:44:26 +0000
Subject: [PATCH 1/3] PolyhedralGeometry: added tutte_lifting(::Graph)

---
 .../Polyhedra/constructions.md                |  1 +
 .../Polyhedron/standard_constructions.jl      | 37 +++++++++++++++++++
 src/exports.jl                                |  1 +
 3 files changed, 39 insertions(+)

diff --git a/docs/src/PolyhedralGeometry/Polyhedra/constructions.md b/docs/src/PolyhedralGeometry/Polyhedra/constructions.md
index c382387c72f9..2a947635d5e6 100644
--- a/docs/src/PolyhedralGeometry/Polyhedra/constructions.md
+++ b/docs/src/PolyhedralGeometry/Polyhedra/constructions.md
@@ -190,6 +190,7 @@ rss_associahedron
 signed_permutahedron
 stable_set_polytope
 transportation_polytope
+tutte_lifting
 zonotope
 zonotope_vertices_fukuda_matrix
 ```
diff --git a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
index 99a1c3e228b3..069c9260be44 100644
--- a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
+++ b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
@@ -2455,3 +2455,40 @@ function vertex_figure(P::Polyhedron{T}, n::Int; cutoff=nothing) where {T<:scala
     Polymake.polytope.vertex_figure(pm_object(P), n - 1; opts...), coefficient_field(P)
   )
 end
+
+@doc raw"""
+    tutte_lifting(G::Graph{Undirected})
+
+Compute a realization of `G` in $\mathbb{R}^3$, i.e., a polyhedron whose edge graph is `G`.  Assumes that `G` is planar, 3-connected, and that is has a triangular facet.
+
+# Examples
+```jldoctest
+julia> G = edgegraph(simplex(3))
+Undirected graph with 4 nodes and the following edges:
+(2, 1)(3, 1)(3, 2)(4, 1)(4, 2)(4, 3)
+
+julia> pG = tutte_lifting(G)
+Polytope in ambient dimension 3
+
+julia> vertices(pG)
+4-element SubObjectIterator{PointVector{QQFieldElem}}:
+ [0, 0, 0]
+ [1, 0, 1//3]
+ [0, 1, 0]
+ [1//3, 1//3, 0]
+
+julia> faces(IncidenceMatrix,pG,1)
+6×4 IncidenceMatrix
+[1, 2]
+[1, 3]
+[1, 4]
+[2, 3]
+[2, 4]
+[3, 4]
+
+```
+"""
+function tutte_lifting(G::Graph{Undirected})
+  pmG = Polymake.graph.Graph{Undirected}(; ADJACENCY=G)
+  return polyhedron(Polymake.polytope.tutte_lifting(pmG))
+end
diff --git a/src/exports.jl b/src/exports.jl
index 0dd3e2c74f0f..efc4e0b3c4e6 100644
--- a/src/exports.jl
+++ b/src/exports.jl
@@ -1638,6 +1638,7 @@ export tropical_variety
 export truncate
 export turn_denominator_into_polyhedron
 export tutte_connectivity
+export tutte_lifting
 export tutte_polynomial
 export twist
 export twisting_sheaf

From 0c9f32dfe7479b9a5c8efe766d7888531b008d7a Mon Sep 17 00:00:00 2001
From: Yue Ren <yue.ren.kl@gmail.com>
Date: Mon, 13 Jan 2025 09:05:46 +0000
Subject: [PATCH 2/3] Update
 src/PolyhedralGeometry/Polyhedron/standard_constructions.jl

Co-authored-by: Benjamin Lorenz <benlorenz@users.noreply.github.com>
---
 src/PolyhedralGeometry/Polyhedron/standard_constructions.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
index 069c9260be44..98be32f5450d 100644
--- a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
+++ b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
@@ -2463,7 +2463,7 @@ Compute a realization of `G` in $\mathbb{R}^3$, i.e., a polyhedron whose edge gr
 
 # Examples
 ```jldoctest
-julia> G = edgegraph(simplex(3))
+julia> G = vertex_edge_graph(simplex(3))
 Undirected graph with 4 nodes and the following edges:
 (2, 1)(3, 1)(3, 2)(4, 1)(4, 2)(4, 3)
 

From df009d98a74160029f18e0614ca9aa037c7f9c09 Mon Sep 17 00:00:00 2001
From: Benjamin Lorenz <benlorenz@users.noreply.github.com>
Date: Mon, 13 Jan 2025 10:36:48 +0100
Subject: [PATCH 3/3] Update
 src/PolyhedralGeometry/Polyhedron/standard_constructions.jl

---
 src/PolyhedralGeometry/Polyhedron/standard_constructions.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
index 98be32f5450d..742fddfb53d9 100644
--- a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
+++ b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
@@ -2490,5 +2490,5 @@ julia> faces(IncidenceMatrix,pG,1)
 """
 function tutte_lifting(G::Graph{Undirected})
   pmG = Polymake.graph.Graph{Undirected}(; ADJACENCY=G)
-  return polyhedron(Polymake.polytope.tutte_lifting(pmG))
+  return Polyhedron{QQFieldElem}(Polymake.polytope.tutte_lifting(pmG), QQ)
 end