For a Museum of Mathematics
fundraiser dinner, I created a series of mathematical table
These are each eight inches in diameter and built on the
hi-def color ZPrinter model 650 from 3DSystems.
They vary in color and style, expressing different
mathematical ideas in sculptural form.
Some, like the above, convey an organic sensibility, while
others are more geometric.
This one has flower-like elements and stem-like arches on the
interior within an overall organization based on the snub
Here is a more geometric form, with nested copies of an
Putting delicate elements on the interior protects them while
giving a sense of depth.
This is another one with a biological flavor. It has a
seedpod-like interior, from which pink star-pods grow.
The outer form suggests a small stellated dodecahedron, but
with a chiral twist.
For those who prefer classic geometric designs, here is is one
of my favorites, the compound of five regular tetrahedra.
These I made in a Leonardo style of open faces, encouraging a
peek into the interior, with enough overlap to hold it all
Here again are five regular tetrahedra in five colors, but now
they float in the interior space without directly touching.
They connect through the exterior rings and stars, which I
lightened to pastel shades to help draw one's focus to the
These sensuous forms convey a delicate warmth on the interior
and a starfish-like icosahedral outside.
It is an updated version of my Mermaid's Delight
One of my favorite four-dimensional forms is the
This baby-blue ball is based on the edges of a perspective
transformation of the 120-cell.
Its 720 pentagons are rounded to circles and ellipses to give
it a softer character (and more engineering strength).
Here is another centerpiece whose foundation is the
120-cell. This time the vertices are hollowed out.
The 10-fold appearance from certain special points of view is
This centerpiece is based on the uniform compound of
forty-eight truncated cubes, projected down from four
dimensions to three.
I shaped it with a chiseled look, to emphasize its polyhedral
basis and colored it with a yellow interior,
ranging through orange and red to a blue exterior, to give a
sense of interior heat and energy.
The inside and outside layers keep switching places in this
It is an updated version of my Knot Structured
Taking the above idea further, here is an even more intricate
tangle of edges, yet icosahedrally symmetric.
You can discover various knots if you follow the blue
lines. (I was after a lizard-like coloring.)
Simple, yet worthy of study. (And not to be confused
with a sepaktakraw ball.)
This is just the five regular tetrahedra again, but turned
Peek inside to see the 3-fold vertices.
Here, I was after a monumental architectural aesthetic (on an
8" scale). All the surfaces are portions of spheres.
(So all the cross sections as it was 3D printed layer-by-layer
have circular boundaries.)
This one is a denser experiment with two interconnected layers
and a surface that alternates between them.
Peering through the holes reveals its yellow interior.
Back to a geometric vein, I like the spiral way in which these
three nested icosidodecahedra connect.
For rainbow fans, here are six nested truncated cuboctahedra.
Again, the spiral way that each layer supports the next inner
layer is worth a look.
This one is very cool for a number of reasons. What I
did for the coloring is to make areas of positive curvature
negative curvature blue, and zero curvature yellow. Then
I tweaked the shape until I liked the coloring pattern.
This undersea ballet pose consists of twelve starfish holding
Perhaps this conveys the feeling of a ball of fire, or solar
storms, or some
Here are six sets of five parallel cylinders. Each set
is orthogonal to a pair of dodecahedron faces.
This was a warm-up to the following one, which has twice as
Now pentagonal prisms alternating in two sizes each intersect
seven prisms of the other colors and the other size.
This consists of two interlocked lattices that are free to
move slightly relative to each other.
It is a fascinating representation of the (10,3)-a lattice,
Thank you 3D Systems for
supporting MoMath by making