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Dr Martin Winter

  A picture of me

Dr Martin Winter

Research Fellow
Office: B2.28
Phone: +44 (0)24 765 23972

I am a postdoc working with Agelos Georgakopoulos. I am funded by the EPSRC grant "Graph Theory in Higher Dimensions".

Research Interests
  • polytope theory (combinatorial and geometric aspects; symmetry, rigidity, skeleta, ...),
  • graph theory (spectral, algebraic, geometric and topological),
  • embeddability of graphs, simplicial complexes, CW-complexes,
  • symmetries of discrete and geometric objects (polytopes, graphs, compexes, ...),
  • algebraic combinatorics (association schemes, distance regular graphs, ...),
  • convex geometry,
  • group theory and representation theory,
  • low dimensional topology.
Publications & Preprints
  • Vertex-Facet Assignments for Polytopes (open access; arXiv)
    with T. Jahn
    Contributions to Algebra and Geometry (2020).
  • Geometry and Topology of Symmetric Point Arrangements (link; arXiv)
    Linear Algebra and its Applications (2021),
  • Classification of Vertex-Transitive Zonotopes (open access; pdf; arXiv)
    Discrete & Computational Geometry (2021),
  • The Edge-Transitive Polytopes that are not Vertex-Transitive (link; arXiv)
    with F. Göring
    Ars Mathematica Contemporanea (2022), doi:10.26493/1855-3974.2712.6be
  • Symmetric and Spectral Realizations of Highly Symmetric Graphs (arXiv)
    Preprint, arXiv:2009.01568, September 2020.
  • Eigenpolytopes, Spectral Polytopes and Edge-Transitivity (arXiv)
    Preprint, arXiv:2009.02179, September 2020.
  • Capturing Polytopal Symmetries by Coloring the Edge-Graph (arXiv)
    Accepted at Discrete & Computational Geometry (2022).
  • (Random) Trees of Intermediate Volume Growth (arXiv)
    with G. Kontogeorgiou
    Preprint, arXiv:2212.01883, December 2022.
    accepted at Eurocomb'23
  • Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints (arXiv)
    Preprint, arXiv:2302.14194, February 2023.
  • Characterizing Clique Convergence for Locally Cyclic Graphs of Minimum Degree d>=6 (arXiv)
    with Anna M. Limbach
    Preprint, arXiv:2305.00503, May 2023
Conferences, Workshops, etc.


  • South Eastern Graph Theory Workshop (Chemnitz)
  • FRICO (Chemnitz), Talk: "Spectral Methods for Symmetric Polytopes"
  • South Eastern Graph Theory Workshop (Freiberg)
  • Geomtry Day (Dresden)


  • Polytope Spring School (Bochum), Talk: "Spectral Methods for Symmetric Polytopes"
  • Summer School on Geometric & Algebraic Combinatorics (GAC, Paris)
  • Discrete Geometry Day^2 (Budapest), Talk: "Spectral Methods for Symmetric Polytopes" (slides)
  • South Eastern Graph Theory Workshop (Chemnitz), Talk: "Edge-Transitive Polytopes"
  • Colloquium on Combiantorics (Kolkom, Paderborn), Talk: "Edge-Transitive Polytopes" (slides)
  • Geometry Day (Jena), Talk: "Edge-Transitive Polytopes"


  • Combinatorial Coworkspace (Kleinwalsertal), Talk: "Inscribed Zonotopes and Hyperplane Arrangements with Congruent Chambers" (slides)
  • DMV Annual Conference (Chemnitz), Talk: "Spectral Graph Theory for Polytopes" (slides)


  • (Polytop)ics (MPI Leipzig, online), Talk: "Capturing Polytopal Symmetries in the Edge-Graph" (slides, video)
  • DMV-ÖMG Annual Conference (Passau)



  • Graph Rigidity and Application (Lancaster), Talk: "Rigidity and Tensegrity of Frameworks from Polytopes" (slides)

Where you can meet me:

Further Material


  1. "Capturing Polytopal Symmetries in the Edge-Graph" (extended slides) from my talk at KTH (Stockholm, Sweden)
  2. "On Symmetry, Rigidity and Spectrum" (slides) from my talk at the "School of Mathematical & Statistical Science" at NUI Galway (Ireland)
  3. "Some Modern Open Problems on Convex Polytopes with Symmetries and Regularities" (slides) from my talk at the "Combinatorics Seminar" at Warwick (UK)
  4. "When Edges shrink then Polytopes become smaller - a proof in geometric polytope theory" (slides) from my talk at Pretoria University (South Africa)
  5. "(Random) Trees of Intermediate Volume Growth" (extended slides) from my talk in the Algorithms and Complexity seminar at Durham University
  6. "On 4-Flat Graphs and the Embeddability of 2-Complexes in Dimension Four" (slides) from my talk in the Discrete Geometry seminar at FU Berlin

PhD Thesis

My thesis "Spectral Realizations of Symmetric Graphs, Spectral Polytopes and Edge-Transitivity" and the slides of my defense talk.


In the winter term 2022 I gave a lecture on "Polytope Theory" as part of the Taught Course Center (TCC, at Bath, Bristol, Imperial, Oxford, Warwick and Swansea)

I am an active user of the StackExchange network (username: M. Winter).
These are links to my mathematical profiles: