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Discrete & Computational Geometry, ISSN 0179-5376, 05/2019, pp. 1 - 32
We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the... 
Rectangles | Quadrilaterals | Parameters
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2012, Volume 229, Issue 1, pp. 79 - 101
We investigate necessary conditions for the existence of projections of polytopes that preserve full -skeleta. More precisely, given the combinatorics of a... 
Dimensional ambiguity | Projection of polytopes | Topological obstructions | Products of simplices | Polyhedral surfaces | Wedge products | Products of polygons | MATHEMATICS | PRODUCTS
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 2/2014, Volume 168, Issue 1, pp. 265 - 289
Two-dimensional affine A-nets in $$3$$ -space are quadrilateral meshes that discretize surfaces parametrized along asymptotic lines. The defining property of... 
Geometry | Discrete asymptotic line parametrization | Discrete differential geometry | Hyperboloids | 65D17 | Mathematics | A-nets | Plücker line geometry | 53A05 | 51M30 | Projective geometry | Plucker line geometry | PRINCIPLES | MATHEMATICS | ORTHOGONAL COORDINATE SYSTEMS | DISCRETE | CURVATURE | LATTICES | GEOMETRY
Journal Article
Mathematische Semesterberichte, ISSN 0720-728X, 10/2012, Volume 59, Issue 2, pp. 145 - 152
Konvexe Polytope, also konvexe Hüllen endlich vieler Punkte im euklidischen Raum, stehen an der Schnittstelle zwischen Geometrie und Kombinatorik. Ziel dieses... 
Mathematics, general | Mathematics
Journal Article
Mathematische Semesterberichte, ISSN 0720-728X, 10/2012, Volume 59, Issue 2, pp. 153 - 153
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 12/2009, Volume 42, Issue 4, pp. 527 - 541
There are d-dimensional zonotopes with n zones for which a 2-dimensional central section has Ω(n d−1) vertices. For d=3, this was known, with examples provided... 
Cuts | Computational Mathematics and Numerical Analysis | Zonotopes | Ukrainian easter egg | Mathematics | Projections | Combinatorics | Complexity | Ukrainian easter egg | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | Polytopes | Geometry
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2017, Volume 2017, Issue 2, pp. 323 - 371
Supercyclides are surfaces with a characteristic conjugate parameterization consisting of two families of conics. Patches of supercyclides can be adapted to a... 
MATHEMATICS | ORTHOGONAL COORDINATE SYSTEMS | DISCRETE | SURFACES
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 4/2011, Volume 151, Issue 1, pp. 155 - 173
We introduce the wedge product of two polytopes. The wedge product is described in terms of inequality systems, in terms of vertex coordinates as well as... 
Geometry | Moduli | Convex polytopes | Surfaces of “unusually high genus” | Wreath products of polytopes | Mathematics | Polyhedral surfaces | 52B70 | Combinatorially regular polyhedral surfaces | 51M20 | Surfaces of "unusually high genus" | MATHEMATICS | 2-MANIFOLDS | SPHERES | DYCK REGULAR MAP | NEIGHBORLY CUBICAL POLYTOPES
Journal Article
Computing and Visualization in Science, ISSN 1432-9360, 2/2010, Volume 13, Issue 2, pp. 99 - 110
This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from... 
Polytopes | 05C10 | Visualization | Computational Mathematics and Numerical Analysis | Simplicial manifolds | 52B11 | Mathematics | Schlegel diagrams | Tight spans of finite metric spaces | 05-04 | Algorithms | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Graphs | Tropical polytopes | 68R10 | Computer Applications in Chemistry
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 6/2007, Volume 159, Issue 1, pp. 221 - 242
We prove that the neighborly cubical polytopes studied by Günter M. Ziegler and the first named author [14] arise as a special case of the neighborly cubical... 
Algebra | Analysis | Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | Polytopes | Sphere
Journal Article
11/2019
We introduce orthogonal ring patterns consisting of pairs of concentric circles generalizing circle patterns. We show that orthogonal ring patterns are... 
Mathematics - Complex Variables
Journal Article
02/2018
We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the... 
Mathematics - Differential Geometry
Journal Article
12/2011
Geometriae Dedicata, 2014, Volume 168, Issue 1, pp 265-289 Two-dimensional affine A-nets in 3-space are quadrilateral meshes that discretize surfaces... 
Mathematics - Differential Geometry
Journal Article
12/2014
Internat. Math. Research Notices, vol. 2017 (2), 323-371 Supercyclides are surfaces with a characteristic conjugate parametrization consisting of two families... 
Mathematics - Differential Geometry
Journal Article
08/2009
We introduce the wedge product of two polytopes. The wedge product is described in terms of inequality systems, in terms of vertex coordinates as well as... 
Journal Article
Berlin, Techn. University, Diss., 2008. 
Dissertation
10/2007
There are d-dimensional zonotopes with n zones for which a 2-dimensional central section has \Omega(n^{d-1}) vertices. For d=3 this was known, with examples... 
Journal Article
2012, ISBN 9783642234347
Gridshell structures made of highly elastic materials provide significant advantages thanks to their cost-effective and rapid erection process, whereby the... 
Basics of Construction | Engineering | Computer-Aided Engineering (CAD, CAE) and Design | Building Construction | Engineering Design
Book Chapter
11/2007
This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from... 
Mathematics - Combinatorics
Journal Article
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