5 papers · 1 filter
Deformations and second-order rigidity of polytopes
Matthias Adrian-Himmelmann, Martin Winter, Zhen Zhang
We study deformations of polytopes that preserve edge lengths and face coplanarities. This gives rise to a notion of rigidity, for which we develop a second-order theory together w…
Rigidity of polytopes with edge length and coplanarity constraints
Matthias Himmelmann, Bernd Schulze, Martin Winter
We investigate a novel setting for polytope rigidity, where a flex must preserve edge lengths and the planarity of faces, but is allowed to change the shapes of faces. For instance…
The canonical form, scissors congruence and adjoint degrees of polytopes
Tom Baumbach, Ansgar Freyer, Julian Weigert +1
We study the canonical form as a valuation in the context of scissors congruence for polytopes. We identify the degree of its numerator - the adjoint polynomial $\operatorname…
When do graph covers preserve the clique dynamics of infinite graphs?
Anna M. Limbach, Martin Winter
We investigate for which classes of (potentially infinite) graphs the clique dynamics is cover stable, i. e., when clique convergence/divergence is preserved under triangular cover…
On 2-complexes embeddable in 4-space, and the excluded minors of their underlying graphs
Agelos Georgakopoulos, Martin Winter
We study the potentially undecidable problem of whether a given 2-dimensional CW complex can be embedded into . We provide operations that preserve embeddability, inc…