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PolyhedralGeometry: added tutte_lifting(::Graph) #4451

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1 change: 1 addition & 0 deletions docs/src/PolyhedralGeometry/Polyhedra/constructions.md
Original file line number Diff line number Diff line change
Expand Up @@ -190,6 +190,7 @@ rss_associahedron
signed_permutahedron
stable_set_polytope
transportation_polytope
tutte_lifting
zonotope
zonotope_vertices_fukuda_matrix
```
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37 changes: 37 additions & 0 deletions src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
Original file line number Diff line number Diff line change
Expand Up @@ -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 = 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)

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{QQFieldElem}(Polymake.polytope.tutte_lifting(pmG), QQ)
end
1 change: 1 addition & 0 deletions src/exports.jl
Original file line number Diff line number Diff line change
Expand Up @@ -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
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