Polyhedron Model-Making Tips
Pictured above are the tools I use for constructing my polyhedra:
- A metal ruler and large doll-making needles for scoring
- Scissors and glue for obvious reasons.
- An old piece of card for putting a blob of glue on. It's almost solid
- Wooden skewers for applying the glue. Possibly not the best
thing, but they were the first thing I found and they worked, so I'm still
using them. They don't require much cleaning like brushes, and stray
bristles don't cause problems either.
- Tweezers, including a long pair with angled tip, for squishing
those tabs together.
- The top cut off a coat hanger, for those hard to reach tabs
(I practically never need this though).
- I also have some wooden clothes pegs, taken apart and put
together backwards as recommended by Magnus Wenninger, for clamping tabs as
they glue (but again, I almost never use these).
- And finally of course, a Buffy pencil case to put these tools
A box with compartments can be very useful too when working on a model
with many different parts.
Here the box contains all the parts required for the
pseudo great rhombicuboctahedron.
To make models, you'll need to start with nets. You can print these out
Score along the edges, cut out the nets leaving tabs around the outside, crease
along all the edges, then glue the pieces together (tab to tab).
Here are a few general tips for building models.
Now go forth and make polyhedra!
- I use paper between 120 and 140 gsm (normal printing paper is 80 gsm).
I used to use Canson's Vivaldi paper, but I'm not sure it was acid
free. Now I use paper from Doggitt Pedigree papers, which have a huge
range and their metallic papers are great.
I find thick card leads to a less accurate model.
Acid-free paper should fade less over the years, especially if the
models get any direct sunlight.
- Be careful to score on the front of the paper for a convex fold
(mountain fold), or on the back for a concave fold (valley fold). Make
tiny pin-pricks at each end of lines to be scored on the back, so you
know where to score. The program has the option to use dashed line
when printing concave edges, but I prefer not to see them in the
finished model. If in doubt about which ones are which, print a page
with dashed lines on normal paper as a reference.
- I use double tabs. This means that I usually leave tabs on all
edges around a net, and glue the tabs to each other where faces meet.
This makes the edges more "symmetrical", since both sides have a tab,
and it is easier to squish the tabs together with a pair of tweezers.
- Where faces attach very sharply (a small dihedral angle), I often use a
single tab, and glue it under the joining face. Otherwise the
final edge becomes too "bulky".
- I usually try to use some kind of internal support to give the model
rigidity. I hate "floppy" polyhedra (eg see the
great hexacronic icositetrahedron).
Stella has a number of features to
help with this, including a mode for creating new polygons inside the
model using existing vertices, which you can print out and glue inside
for support. A lot of people use thicker card than me and don't seem
to worry about this though.
- When gluing a part behind a surface that will be visible (eg when
using single tabs, or for extra support, eg see the
great dodecahedron), don't put the glue
behind the visible surface. Instead put it on the surface being glued
to it (the tab). This is because sometimes the moisture in the glue
can cause wrinkling, and it's better to avoid any wrinkles in the
visible surfaces. Also, don't put glue all over largish areas, just
near their edges, to avoid further wrinkling.
- How do you glue the last piece in?!
- Gluing the last piece in can be tricky, because you can't get
inside to squeeze the tabs together. Here again I recommend the
double tab method. Gluing tabs to each other rather than
gluing one tab under the neighbouring surface halves the angle
between the surfaces being glued, so the paper's natural
springiness helps to push those tabs together.
- If the last flap is a pentagon, say, then one edge is already
connected and four others remain to be glued. You could try gluing
another two of these, one at a time, if your model flexes enough to
still allow you to get glue onto the last tabs afterwards, but your
paper may get bent and creased. I would usually put glue on all
the remaining edges and do them all at once. If using double tabs,
I'd recommend alternating glue on the top or bottom tab in each
pair. Experience says it produces more even results, as there's no
imbalance between the parts being glued, which can lead to edges
not quite aligning before the glue locks things in place.
- Finally, you often need to figure out how to get that last piece in
on a case-by-case basis. I've documented this for various models
I've made. Here are some models where extra thought had to be put
in to figure out how to finish them off.