13 papers
Polyhedral Maps of Cubic Graphs with given Automorphism Groups
Ugo Detaille, Meike Weiß, Reymond Akpanya +1
L. Babai introduced a method for constructing a cubic graph whose automorphism group is isomorphic to a given finite group , obtained by modifying a corresponding Cayley graph o…
An algorithmic approach for computing fundamental domains of crystallographic groups
Reymond Akpanya, Alice C. Niemeyer, Lukas Schnelle
A crystallographic group is a discrete subgroup of the Euclidean group that has a compact fundamental domain. Since such a crystallographic group is infin…
Strong Embeddings of Regular Graphs with Prescribed Automorphism Groups
Reymond Akpanya, Tom Goertzen, Meike Weiß
A classical theorem of Frucht states that every finite group occurs as the automorphism group of a finite graph. We prove an embedded analogue for regular graphs of arbitrary degre…
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…
Influence of a generative parameter on the mechanical performance of topological interlocking assemblies of a hexagonal block
Lukas Schnelle, Meike Weiß, Reymond Akpanya +2
A topological interlocking assembly is an arrangement of blocks, where all blocks are kinematically constrained by their neighboring blocks and a fixed frame. This concept has been…
A Census of Edge-transitive Surfaces
Reymond Akpanya
In this paper, we study edge-transitive surfaces, i.e. triangulated 2-dimensional manifolds whose automorphism groups act transitively on the edges of these triangulated surfaces.…
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…
A census of face-transitive surfaces
Reymond Akpanya, Jonathan Spreer
A face-transitive surface is a triangulated 2-dimensional manifold whose automorphism group acts transitively on its set of triangles. In this paper, we investigate this class of h…
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…
On inside-out Dissections of Polygons and Polyhedra
Reymond Akpanya, Adi Rivkin, Frederick Stock
In this work we study inside-out dissections of polygons and polyhedra. We first show that an arbitrary polygon can be inside-out dissected with pieces, thereby improving th…
Topologically Interlocking Blocks inside the Tetroctahedrille
Reymond Akpanya, Tom Goertzen, Alice C. Niemeyer
A topological interlocking assembly consists of rigid blocks together with a fixed frame, such that any subset of blocks is kinematically constrained and therefore cannot be remove…
Surfaces with given Automorphism Group
Reymond Akpanya, Tom Goertzen
Frucht showed that, for any finite group , there exists a cubic graph such that its automorphism group is isomorphic to . For groups generated by two elements we simplify his…