# Mircea Draghicescu

Portland, Oregon, USA

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.

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.

Duality 1

22 x 22 x 22 cm

vellum paper

2016

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).

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).

Duality 2

34 x 34 x 34 cm

vellum paper

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.

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.