38 citations · 130 across the 21 of their papers we have counts for
23 papers
Pentagonal bipyramids lead to the smallest flexible embedded polyhedron
Matteo Gallet, Georg Grasegger, Jan Legerský +1
Steffen's polyhedron was believed to have the least number of vertices among polyhedra that can flex without self-intersections. Maksimov clarified that the pentagonal bipyramid wi…
Calligraphs and sphere realizations
Matteo Gallet, Georg Grasegger, Niels Lubbes +1
We introduce a recursive procedure for computing the number of realizations of a minimally rigid graph on the sphere up to rotations. We accomplish this by combining two ingredient…
Zero-sum cycles in flexible non-triangular polyhedra
Matteo Gallet, Georg Grasegger, Jan Legerský +1
Finding necessary conditions for the geometry of flexible polyhedra is a classical problem that has received attention also in recent times. For flexible polyhedra with triangular…
A new line-symmetric mobile infinity-pod
Matteo Gallet, Josef Schicho
We construct parallel manipulators with one degree of freedom and admitting infinitely many legs lying on a curve of degree ten and genus six. Our technique relies upon a duality b…
Hexapods with a small linear span
Hans-Christian Graf von Bothmer, Matteo Gallet, Josef Schicho
The understanding of mobile hexapods, i.e., parallel manipulators with six legs, is one of the driving questions in theoretical kinematics. We aim at contributing to this understan…
Zero-sum cycles in flexible polyhedra
Matteo Gallet, Georg Grasegger, Jan Legerský +1
We show that if a polyhedron in the three-dimensional affine space with triangular faces is flexible, i.e., can be continuously deformed preserving the shape of its faces, then the…
Combinatorics of Bricard's octahedra
Matteo Gallet, Georg Grasegger, Jan Legerský +1
We re-prove the classification of flexible octahedra, obtained by Bricard at the beginning of the XX century, by means of combinatorial objects satisfying some elementary rules. Th…
On the existence of paradoxical motions of generically rigid graphs on the sphere
Matteo Gallet, Georg Grasegger, Jan Legerský +1
We interpret realizations of a graph on the sphere up to rotations as elements of a moduli space of curves of genus zero. We focus on those graphs that admit an assignment of edge…
Reconstruction of rational ruled surfaces from their silhouettes
Matteo Gallet, Niels Lubbes, Josef Schicho +1
We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the `apparent contour' of a single projection to the projective plane. We de…
Counting realizations of Laman graphs on the sphere
Matteo Gallet, Georg Grasegger, Josef Schicho
We present an algorithm that computes the number of realizations of a Laman graph on a sphere for a general choice of the angles between the vertices. The algorithm is based on the…
Reconstruction of surfaces with ordinary singularities from their silhouettes
Matteo Gallet, Niels Lubbes, Josef Schicho +1
We present algorithms for reconstructing, up to unavoidable projective automorphisms, surfaces with ordinary singularities in three dimensional space starting from their silhouette…
Probabilities of incidence between lines and a plane curve over finite fields
Mehdi Makhul, Josef Schicho, Matteo Gallet
We study the probability for a random line to intersect a given plane curve, defined over a finite field, in a given number of points defined over the same field. In particular, we…
Counting projections of rational curves
Matteo Gallet, Josef Schicho
Given two general rational curves of the same degree in two projective spaces, one can ask whether there exists a third rational curve of the same degree that projects to both of t…
The number of realizations of a Laman graph
Jose Capco, Matteo Gallet, Georg Grasegger +3
Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph…
Mobile Icosapods
Matteo Gallet, Georg Nawratil, Josef Schicho +1
Pods are mechanical devices constituted of two rigid bodies, the base and the platform, connected by a number of other rigid bodies, called legs, that are anchored via spherical jo…
The diffeomorphism type of small hyperplane arrangements is combinatorially determined
Matteo Gallet, Elia Saini
It is known that there exist hyperplane arrangements with same underlying matroid that admit non-homotopy equivalent complement manifolds. In this work we show that, in any rank, c…
Varieties of apolar subschemes of toric surfaces
Matteo Gallet, Kristian Ranestad, Nelly Villamizar
Powersum varieties, also called varieties of sums of powers, have provided examples of interesting relations between varieties since their first appearance in the 19th century. One…
Liaison Linkages
Matteo Gallet, Georg Nawratil, Josef Schicho
The complete classification of hexapods - also known as Stewart Gough platforms - of mobility one is still open. To tackle this problem, we can associate to each hexapod of mobilit…
Planar Linkages Following a Prescribed Motion
Matteo Gallet, Christoph Koutschan, Zijia Li +3
Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also…
Ambiguities in a Problem in Planar Geodesy
Josef Schicho, Matteo Gallet
This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean pl…
Möbius Photogrammetry
Matteo Gallet, Georg Nawratil, Josef Schicho
Motivated by results on the mobility of mechanical devices called pentapods, this paper deals with a mathematically freestanding problem, which we call Möbius Photogrammetry. Unlik…
Bond theory for pentapods and hexapods
Matteo Gallet, Georg Nawratil, Josef Schicho
This paper deals with the old and classical problem of determining necessary conditions for the overconstrained mobility of some mechanical device. In particular, we show that the…
On Computing the Elimination Ideal Using Resultants with Applications to Gröbner Bases
Matteo Gallet, Hamid Rahkooy, Zafeirakis Zafeirakopoulos
Resultants and Gröbner bases are crucial tools in studying polynomial elimination theory. We investigate relations between the variety of the resultant of two polynomials and the v…