# Mircea Draghicescu

I like to design new and easy to reproduce methods for building
geometric models that can be used not only to create mathematical art
sculptures, but also to teach and inspire a large audience.

The general technique illustrated here is based on connecting, without
glue, multiple copies of a single construction element. The elements
can be made from a variety of materials and can have many shapes that
produce different artistic effects.

The constructs are models of dual compounds; in principle, any dual
compound can be modeled in this manner, subject to some physical
limitations. The construction method and underlying geometry are
presented in a workshop at Bridges 2016.

This is a model of the icosidodecahedron / rhombic triacontahedron
dual compound, built using 60 elements connected at 62 nodes.

In general, the number of connection nodes is 2 + the number of
construction elements whenever the modeled polyhedra satisfy
Euler's formula.

The coloring scheme with 6 colors, emphasizes the dodecahedral
aspect: the connection nodes corresponding to the pentagonal faces
of the icosidodecahedron (or, same thing, the vertices of the
rhombic triacontahedron with 5 adjacent edges) are clearly
visible.

This is a model of the icosahedron / dodecahedron dual
compound.

It is built using 30 construction elements, each representing a
polyhedron edge and the corresponding dual edge.

The construction elements are 12 cm in diameter and have 4
connection points corresponding to the endpoints of the two
modeled edges.

The entire model has 32 connection nodes corresponding to either
the faces of the two polyhedra, or (by duality) their vertices.

I used here 5 colors, with the 6 elements of one color at the
vertices of an octahedron.

5 elements of different colors come together at each of the 12
connection nodes corresponding to the vertices of the icosahedron
(or, same thing, the faces of the dodecahedron).