A PARADE OF
PROJECTIONS
“From geometric exercise we get
things that are more and more
artistic”
Carlo Séquin
G
3D
eometry has been in Carlo
Séquin’s blood since the 11th
grade, when one of his assignments
was to construct the lines of
intersection between two cylinders.
This early assignment – to represent
a mathematical concept as a tangible
object – was the beginning of Séquin’s
fascination with, what he calls, artistic
geometry.
4D
5D
In his Bridges lecture, Séquin
explained how all five regular 3D
polyhedra (such as the cube) can be
constructed from 2D regular polygons
(6 squares make up a cube). From 2D
to 3D this is easily visualized, but what
about in higher dimensions? Although
geometric reasoning can show
convincingly that there are exactly six
regular polytopes (higher dimension
equivalent of a polyhedron) in 4D that
can be constructed from 3D polyhedra,
you will understandably have a harder
time picturing this.
To visualize 4D objects, we need
to rely on wireframe projections—