Objective: Build
a simple desktop dome or sphere using circles formed into triangles.
Materials:
| compass | scissors | glue |
| thick paper | ruler | pencil |
| glue |
Concepts: equilateral triangles, geodesic surfaces, counting, circles, chords
This model introduces younger students to the concept of domes constructed
of triangles, and can be easily scaled to larger sizes to build cardboard
clubhouses, planetariums, art projects, and spheres. The size is only limited
by the strength of your building materials. In technical terms, this is a one-frequency
geodesic dome, or a dodecahedron (if fully assembled).
1. Draw 20 identical circles. You can make the
circles out of paper, construction paper, or cardboard. You can
draw the circles by using a compass, or tracing a can, or whatever
method suits you. Cut each out carefully. 
2. Fold each circle into the shape of an equilateral
triangle as shown below.
3. Arrange five triangles into a pattern as shown below.
4. Unfold the adjacent
flaps and glue them together. When the glue is dry enough to take
the stress, glue the final two flaps together by lifting the center
of the construction together to form a little cap. Then the two remaining
flaps can be brought together to be permanently attached. If you
want the flaps on the inside (not suitable for planetariums, but
better if you want to make a sphere) you must pop the center of the
cap down, rather than up, when making the final attachment.
This is what the finished cap (with flaps on the outside) should look like:
5. Make another cap with five more triangles.
6. Arrange the remaining 10 triangles into an alternating pattern like this, gluing adjacent flaps.
7. Form this strip of 10 triangles into a ring, with flaps in or out to match the caps you made earlier. You will notice that on the top of the ring has 5 flaps, and so does the bottom of the cap. Match them up and glue them together and you will have a little planetarium dome model made of one type of triangle!
8. Put the remaining cap on the bottom of the ring to make a dodecahedron.
For a projector dome with a smooth interior surface, put the
flaps outward.
For a sphere or dodecahedron with a smooth exterior surface, put
the flaps inward
Figures adapted from a diagram at www.desertdomes.com.
Your project is complete!