# Astral (n 4 ) Configurations

@inproceedings{GrnbaumAstral4, title={Astral (n 4 ) Configurations}, author={Branko Gr{\"u}nbaum} }

A family of n points and n (straight) lines in the Euclidean plane is said to be an (n 4) configuration provided each point is on four of the lines and each line contains four of the points. A configuration may have various symmetries, that is, there may exist isometric mappings of the plane onto itself that map the configuration onto itself; all the symmetries of a configuration form its group of symmetries. It is obvious that no more than two points of a line can be in the same transitivity…

## 9 Citations

Which (n 4 ) Configurations Exist ?

- Mathematics

An (n k) configuration is a family of n points and n (straight) lines in the Euclidean plane such that each point is on precisely k of the lines, and each line contains precisely k of the points.…

Connected ( n k ) configurations exist for almost all n

- Mathematics
- 2021

A geometric (nk) configuration is a collection of points and straight lines, typically in the Euclidean plane, so that each line passes through k of the points and each of the points lies on k of the…

Even Astral Configurations

- MathematicsElectron. J. Comb.
- 2004

This paper completes the classification of all even astral configurations and defines an astral configuration configuration whereq and k are both even.

Some Results on Odd Astral Configurations

- MathematicsElectron. J. Comb.
- 2006

All known results in the classification of odd astral configurations where $q$ and $k$ are both at least 4 are presented.

Constructing 5-Configurations with Chiral Symmetry

- MathematicsElectron. J. Comb.
- 2010

This work describes how to construct the first known family of $5-configurations with chiral (that is, only rotational) symmetry, and proves that the construction works; in addition, the construction technique produces the smallest known geometric 5- configuration.

A Characterization of Astral (n4) Configurations

- Mathematics, PhysicsDiscret. Comput. Geom.
- 2001

A conjecture of Branko Grünbaum concerning what astral (n4) configurations exist is shown to be true.

Movable (n4) Configurations

- MathematicsElectron. J. Comb.
- 2006

A tantalum capacitor comprising a cylindrical body and an axial tantalum anode wire. This wire is first folded and then soldered to an anode connection wire roughly parallel to a cathode connection…

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