# Configurations of Points and Lines

@inproceedings{Grnbaum2009ConfigurationsOP, title={Configurations of Points and Lines}, author={Branko Gr{\"u}nbaum}, year={2009} }

This is the only book on the topic of geometric configurations of points and lines. It presents in detail the history of the topic, with its surges and declines since its beginning in 1876. It covers all the advances in the field since the revival of interest in geometric configurations some 20 years ago. The author's contributions are central to this revival. In particular, he initiated the study of 4-configurations (that is, those that contain four points on each line, and four lines through…

## 144 Citations

### Geometric constructions for 3-configurations with non-trivial geometric symmetry

- Mathematics
- 2013

A geometric 3-configuration is a collection of points and straight lines, typically in the Euclidean plane, in which every point has 3 lines passing through it and every line has 3 points lying on…

### Sparse line deletion constructions for symmetric 4-configurations

- MathematicsArs Math. Contemp.
- 2015

This paper introduces a new family of 4-configurations, a collection of points and lines in the Euclidean plane such that each point lies on four lines and each line passes through four points, and generalizes a 2010 result of Berman and Grunbaum.

### Exploring the infinitesimal rigidity of planar configurations of points and rods

- Mathematics
- 2021

This article is concerned with the rigidity properties of geometric realizations of incidence geometries of rank two as points and lines in the Euclidean plane; we care about the distance being…

### Platonic configurations of points and lines

- Mathematics
- 2019

We present some methods for constructing connected spatial geometric configurations (pq, nk) of points and lines, preserved by the same rotations (and reflections) of Euclidean space E as the chosen…

### Configurations of higher orders

- Mathematics
- 2022

This paper begins by extending the notion of a combinatorial conﬁguration of points and lines to a combinatorial conﬁguration of points and planes that we refer to as conﬁgurations of order 2 . We…

### Geometric Constructions for Symmetric 6-Configurations

- Mathematics
- 2014

This article surveys several known geometric construction techniques that produce highly symmetric 6-configurations, a collection of points and lines typically in the Euclidean plane.

### On the configurations of nine points on a cubic curve

- MathematicsAustralas. J Comb.
- 2021

The reciprocal position of nine points in the plane is studied, according to their collinearities, and the possible Hilbert functions of the ideals of the nine points are computed.

### An infinite class of movable 5-configurations

- MathematicsArs Math. Contemp.
- 2016

A construction is developed that produces infinitely many new 5-configurations which are movable and with one continuous degree of freedom for all odd k > 2 .

### Polycyclic Movable 4-Configurations are Plentiful

- MathematicsDiscret. Comput. Geom.
- 2016

A method for constructing a large number of new infinite families of rotationally symmetric geometric 4-configurations which are movable; that is, there is at least one continuous parameter which preserves the symmetry of the configuration.

### Line arrangements with the maximal number of triple points

- Mathematics
- 2016

The purpose of this note is to study configurations of lines in projective planes over arbitrary fields having the maximal number of intersection points where three lines meet. We give precise…