Morton C. Bradley (1912-2004)
was
well known as an art conservator but not sufficiently well
known for
his geometric sculpture. After his death, his large corpus of
sculpture
and models went to Indiana University. See the
IU
web
site for photos of his work and information about his
life
and the fabricators who worked with him to produce these
designs.
Most of Bradley's sculpture involved polyhedra-based
constructions with
color patterns based on the Munsell color sphere. I have
re-created some of the forms with additive
fabrication
technology, addressing the geometry but not the color
aspect of his work. This page
briefly discusses five of his designs. Much more could
be said,
but my purpose here is to say
just enough to get more people aware of and interested in his
work. The stl
files for the five models illustrated here can be downloaded,
so anyone
with access to a 3D printer can reproduce them. The stl
files can
also be viewed and rotated in an stl viewer to get a good
sense of the
3D structure. Images of the five original Bradley sculptures
below are
used by permission of the Indiana University Art Museum.
Untitled 1971
The above model illustrates the form of Untitled 1971. It
is composed
of twelve corner-connected small
stellated
dodecahedra, centered on the twelve vertices of an imagined
icosahedron.
The original is 20" in diameter, made of 2-ply paper. The
models
shown on this page are each about 3 inches in diameter, made
of
nylon by
selective laser sintering.
Like any good sculpture, this work has many different views,
depending
on the position of the viewer. In the above view, the camera
is looking
along a 3-fold axis. Compare it to the
similar
view
in
the
IU slideshow. Ideally the units would each
touch five neighbors at a mathematical point. Bradley's
original paper
sculpture could be held together and aligned by means of rigid
wires
that pass through the connection points. In these small
versions,
I approximate that by having the tips of the small stellated
dodecahedra overlap their neighbors slightly. I tried to make
the
smallest possible overlap which allows the construction to
hold
together; so these models should be handled gently.
If one looks down a 5-fold axis, then Untitled
1971 appears as above. With access to a 3D printer,
you can use this stl file to make
your own copy.
An important point to notice is that the twelve units of Untitled 1971 are not
parallel. The rendering at right shows a similar form
also
consisting
of twelve small stellated dodecahedra positioned at the
vertices of an
imagined icosahedron, but where the planes are parallel.
In
polyhedral assemblages of this sort, there are two possible
orientations
which preserve the overall rotational and mirror symmetry.
These differ
in that each unit in the
more structured version at right is rotated 36 degrees
relative to the
corresponding unit in the more open version at
left. Bradley chose the more directionally
varied
design on the left.
Circus
The form of Circus is
also
an assemblage of corner-connected small stellated dodecahedra.
In this
case there are
twenty units instead of twelve. Each is centered on the
vertices of an imagined dodecahedron. A photo of the original
24" paper
sculpture can be found here.
While
Bradley's
piece
is designed to hang, a pleasing property of this
structure is that it stands beautifully on three points
(assuming you
have
a rigid, accurate model). So it has twenty built-in stands.
Again, different viewpoints have very different effects. In
the above
image, we look down a 3-fold axis.
And above, Circus is viewed along a 5-fold axis. The stl
file is here.
Again, there are two possible symmetry-preserving ways to
choose the
orientation of the components, as shown above. In the one at
left
above, all the units are
parallel. At right, they have each been rotated 60 degrees, so
are not
parallel. Unlike Untitled
1971,
for Circus, Bradley's
version
is
the one in which the units are parallel.
Archimedes
In a very different style, the form of Archimedes is based on a
truncated
icosidodecahedron which has been augmented with halves of
icosidodecahedra, halves of cuboctahedra, and halves of
octahedra. The
original is painted plastic, 15" in diameter. It has a
massive
feeling when made in a solid color, but see the image in the
IU
slideshow to appreciate the very different visual impact
the
form acquires when painted in Bradley's color scheme.
The stl file is here.
There are four different ways to attach the half polyhedra and
still
maintain the overall symmetry. Can you detect the subtle
differences among these four and point out which Bradley
chose?
Untitled 1977
Untitled 1977 is an
assemblage
of twelve great dodecahedra joined along edges. Again,
the
centers are placed at the vertices of an imagined
icosahedron. (I
don't see a photo of this on the IU site to compare.)
The
stl file is here.
Above is the view along a 5-fold axis. Notice how the twelve
modules
each contribute one pentagon of a dodecahedron which seals off
a space
in the
inteior.
It is interesting to visualize the shape of the
trapped
volume. It is like a dodecahedron with a star chiseled
into each
face.
Harlequin
The form of Harlequin is
based
on a great stellated dodecahedron. It also does not
currently appear to be on the IU web page, so I can not point
you to a
comparison image. One side of each star arm is cut away,
as in
Escher's Gravity. In
its
place is a triangular surface which connects that outer edge
to the
center of the
form, as in Alan Holden's nolids.
There is a nice
pinwheel-like
chirality to the
form, as this view down a 5-fold axis shows. The stl
file
to make your own copy is here.
This two-coloring is not
the same
as Bradley's color scheme, but suggests a kind of jester's
hat, which
should make clear why the name Harlequin
is appropriate for the
structure.
Notes
The above is just an introduction. There are many
other
interesting sculptures by Morton Bradley, which I should write
about
elsewhere. There are also many possible variations
on these
design ideas.