
 Compound of 5 Tetrahedra 
This compound of 5 tetrahedra is an old
favourite among geometers, having first been described by Edmund Hess in 1876.
Can you spot a tetrahedron in each color as they weave through each other?
The model is provided in Small Stella,
Great Stella and
Stella4D's Polyhedron Libraries. It is a
stellation of the
icosahedron (the face planes carve out an
icosahedron at the centre), and a faceting of the
dodecahedron (they share the same vertex
positions). This model is just 10cm in diameter.

The stellation diagram of the icosahedron, with the appropriate cells
selected to generate the compound of 5 tetrahedra. You can create the
compound yourself using Great Stella or Stella4D's stellation tools.


The nets printed onto metallic paper. I suggest printing out an extra
1 or 2 nets of each color, as you will need to butcher a couple near
the end.


A couple of nets printed, scored, cut out, and folded. 20 of these are
required, 4 in each of 5 colors.


Two parts complete.


First 3 parts glued together. Be careful to attach them correctly!


First 5 parts viewed from below. After this be careful to follow the
color scheme set out so far.


At this stage just 5 parts remain to be done. However given the twisty
gnarled nature of the parts, some thought has to go into how to
proceed. It would be almost impossible to continue attaching one part
at a time!


I decided to continue with this partial crown, over which I could fit
the final cap. Butcher the original nets to create these parts. I
also printed out some extra white triangles to fit inside each part,
creating a solid surface for the final cap to glue onto. These extra
triangles were created and printed using Stella's Faceting mode.


Here's the final cap. Each color uses just 2 of the 3 original faces
from each net, plus some more of the white triangles used above. This
cap then fits snuggly over the above crown. The white triangles glue
together in one go, then there are 5 colored flaps to glue down one at
a time.
This worked pretty well, though I now wonder if a better way would
be to create the final cap complete, using the full 3 faces from 5
nets, but have that part extend into the rest of the model a bit to
slide it into place. But then maybe the 5fold dimples wouldn't end up
so neat that way. Hmm, it's a tricky model to finish well!

