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Danzer’s configuration revisited
Dedicated to the memory of Ludwig Danzer (1927–2011)
-
Marko Boben
und
Tomaž Pisanski
Veröffentlicht/Copyright:
6. Oktober 2015
Abstract
We revisit the configuration DCD(4) of Danzer, a great inspiration for our work. This configuration of type (354) falls into an in_nite series of geometric point-line configurations DCD(n). Each DCD(n) is characterized combinatorially by having the Kronecker cover over the Odd graph On as its Levi graph. Danzer’s configuration is deeply rooted in Pascal’s Hexagrammum Mysticum. Although the combinatorial configuration is highly symmetric, we conjecture that there are no geometric point-line realizations with 7- or 5-fold rotational symmetry; on the other hand, we found a point-circle realization having the symmetry group D7, the dihedral group of order 14.
Keywords: Danzer configuration; Danzer graph; Odd graph; Kronecker cover,V-construction,Hexagrammum Mysticum; point-circle configuration; Cayley-Salmon configuration; Steiner-Plücker configuration; Coxeter (283)-configuration
Received: 2013-1-7
Revised: 2014-10-24
Published Online: 2015-10-6
Published in Print: 2015-10-1
© 2015 by Walter de Gruyter Berlin/Boston
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Artikel in diesem Heft
- Frontmatter
- Danzer’s configuration revisited
- Sasaki manifolds with positive transverse orthogonal bisectional curvature
- Real open books and real contact structures
- Locally Monge–Ampère parabolic foliations
- Gradient estimates for the heat equation under the Ricci-harmonic map flow
- The Log-Convex Density Conjecture and vertical surface area in warped products
- Further properties of the Bergman spaces of slice regular functions
- Constructions of complete sets
- The Euclidean distortion of generalized polygons
- On the geometrical properties of solvable Lie groups
- Another proof of the Beckman–Quarles theorem
Artikel in diesem Heft
- Frontmatter
- Danzer’s configuration revisited
- Sasaki manifolds with positive transverse orthogonal bisectional curvature
- Real open books and real contact structures
- Locally Monge–Ampère parabolic foliations
- Gradient estimates for the heat equation under the Ricci-harmonic map flow
- The Log-Convex Density Conjecture and vertical surface area in warped products
- Further properties of the Bergman spaces of slice regular functions
- Constructions of complete sets
- The Euclidean distortion of generalized polygons
- On the geometrical properties of solvable Lie groups
- Another proof of the Beckman–Quarles theorem
