7 papers
Construction Methods for Space-Filling Heterogeneous Topological Interlocking Assemblies
Meike Weiß, Alice C. Niemeyer
Deforming fundamental domains of wallpaper groups provides a systematic way to generate non-convex blocks which admit topological interlocking assemblies (TIAs). We use this approa…
Influence of the geometry on the mechanical performance of tubular interlockings: A study of the Sine Block
Domen Macek, Meike Weiß, Reymond Akpanya +3
Topological interlocking assemblies (TIA) are arrangements of blocks such that rigid-body motions of the blocks are fully constrained by their neighbours and a fixed frame. In this…
On 3-Connected Planar Graphs with Unique Orientable Circuit Double Covers
Meike Weiß, Reymond Akpanya, Alice C. Niemeyer
A circuit double cover of a bridgeless graph is a collection of even subgraphs such that every edge is contained in exactly two subgraphs of the given collection. Such a circuit do…
On 3-Connected Cubic Planar Graphs and their Strong Embeddings on Orientable Surfaces
Meike Weiß, Reymond Akpanya, Alice C. Niemeyer
Although the strong embedding of a 3-connected planar graph on the sphere is unique, can have different inequivalent strong embeddings on a surface of positive genus. If $G…
Construction of Toroidal Polyhedra corresponding to perfect Chains of wild Tetrahedra
Reymond Akpanya, Vanishree Krishna Kirekod, Alice C. Niemeyer +1
In 1957, Steinhaus proved that a chain of regular tetrahedra, meeting face-to-face and forming a closed loop does not exist. Over the years, various modifications of this statement…
Interplay of Cubic Graphs and Simplicial Surfaces
Meike Weiß, Alice C. Niemeyer
Simplicial surfaces describe the incidence relations between vertices, edges and faces of triangulated 2-dimensional manifolds in a purely combinatorial way. By considering only th…