Compound of 10 Tetrahedra
Another classic compound is the compound of 10
compound of 5 tetrahedra is chiral, i.e. it doesn't have
any mirror symmetry and comes in left- and right-handed versions. If you
combine these together you get this compound of 10 tetrahedra. You may also
think of this as a compound of 5 stella octangula
(5 compounds of 2 tetrahedra).
Can you spot a tetrahedron in each color? This model is made in 10 colors,
one for each tetrahedron. But I also grouped the colors roughly into two sets
of 5, one lighter and one darker, each representing one compound of 5
tetrahedra. Doing this means that dark only touches light and vice versa.
I also went for matching pairs between the sets:
Each pair represents a stella octangular. This also guarantees that the light
and dark versions of colors never touch each other.
- Light blue and dark blue
- Light green and dark green
- Light pink and dark red
- Light silver and dark grey
- Light yellow and dark purple (ran out of matching paper colors here!)
You could also make interesting models with either 5 colors or just 2 colors.
5 colors would highlight each stella octangula, or 2 colors would highlight
the two mirror image compounds of 5 tetrahedra.
The compound is also a stellation of the
icosahedron (the facial planes carve out an
icosahedron at the centre), and a faceting of the
dodecahedron (they share the same vertex
The model and the nets required to build it are available in
Small Stella, Great Stella and Stella4D's Polyhedron Libraries.
This paper model is 14cm in diameter.
Start gluing the parts together, but be very careful to get the color
I used Stella's Faceting mode to create some extra pieces to fit inside
and add strength, seen here in white.
About half-way. Keep adding the internal parts as long as you can
still reach inside. Make sure you have some angled needle-nose
When arriving at the last 5 peaks, you'll need to proceed a little
differently. From this point, I made the 5 peaks individually, along
with those internal pieces to hold their shape on each side. You can
then glue these in one by one.
Here's a close-up of those final pieces.