Leah Wrenn Berman

Geometric "Floral" configurations

With an increase in size, configurations of points and lines in the plane usually become complicated and hard to analyze. The floral configurations we are introducing here represent a new type that makes accessible and visually intelligible even configurations of considerable size. This is achieved by combining a large degree of symmetry with a hierarchical construction. Depending on the details of the interdependence of these aspects, there are several subtypes that are described and investigated.

A New Class of Movable (n4) Configurations

A geometric (n 4 ) configuration is a collection of n points and n lines, usually in the Euclidean plane, so that every point lies on four lines and every line passes through four points. This paper introduces a new class of movable ((5m) 4 ) configurations---that is, configurations which admit a continuous family of realizations fixing four points in general position but moving at least one other point---including the smallest known movable (n 4 ) configuration.

Graphs with Obstacle Number Greater than One

An emph{obstacle representation} of a graph

Linear astral (n5) configurations with dihedral symmetry

G

Fully truncated simplices and their monodromy groups

is a straight-line drawing of

Operations on Oriented Maps

G

Movable

in the plane together with a collection of connected subsets of the plane, called emph{obstacles}, that block all non-edges of

(n_{4})

G

Configurations

while not blocking any of the edges of

Movable (n4) Configurations

G