Pyramids and other solid shapes
What’s this? It looks like a design made out of triangles. Well, it
is—but it’s also something that you can make into something else!
Trace the design on a piece of paper and then cut it out. If you want to
make a much stronger construction, you can glue your tracing on
construction paper before you cut it out. Fold the paper on the dotted
lines. Then open the paper and fold the flaps down.
Working with one flap at a time, put a bit of glue on each flap, then
stick the flap to the
Make your own tetrahedron by tracing this pattern.
Follow the directions on these pages.
tetrahedrons
underside of the triangle next to it. You’ll easily be able to tell
where the flaps go. When you’ve done all this, you’ll find that you have
made a sort of pyramid. A shape of this kind, with four triangular sides
that are exactly the same, is called a tetrahedron (teht ruh
[hee]{.smallcaps} druhn).
A tetrahedron is what is called a solid shape. It is a shape that has
three dimensions—length, width, and thickness. A flat shape, such as a
triangle, has only length and width. The piece of paper you used is a
flat shape. And the four triangles on the paper are also flat shapes.
Yet, you made a solid shape. And the fact is, a great many solid shapes
can be made out of flat shapes.
Make your own cube by tracing this pattern. Follow the directions on
the opposite page.
Long ago, in ancient Greece, a group of men who spent most of their time
studying numbers and shapes discovered how to make many solid shapes out
of flat shapes. Some of the things they discovered are surprising. You
might have fun trying to make some of the things they did.
For example, these six squares will make a shape that you know quite
well—a cube.
Cut out the shape and fold the paper on the dotted lines. Then glue each
of the flaps to an underside of a square (once again, you’ll easily be
able to tell where the flaps go).
cubes
octahedrons
Here’s another shape made of triangles. It’s a little harder to make
than the other two. But if you can do it, you’ll find you’ve made a
shape called an octahedron (ahk tuh HEE druhn), a shape that has eight
flat faces, or sides.
The octahedron may look familiar to you. It looks like a diamond. And,
as a matter of fact, real diamonds are often found in the shape of an
octahedron.
Make your own octahedron by tracing this pattern. Fold and glue the
flaps just as you did for the tetrahedron and cube.
Here’s a pattern for making still another solid shape out of triangles.
It’s even harder to make than an octahedron, but if you can make it,
you’ll have a shape with twenty equal sides— an icosahedron (eye koh
suh HEE druhn).
icosahedrons
Make your own icosahedron by tracing this pattern. Trace the solid
lines, dotted lines, and letters. Fold inward along the dotted lines.
Starting with flap A, glue the back of flap A to the edge marked A.
Then, keep going, following the alphabet.
Make your own dodecahedron by tracing this pattern. Trace the solid
lines, dotted lines, and letters. Fold inward along the dotted lines.
Starting with flap A, glue the back of flap A to the edge marked A.
Then, keep going, following the alphabet.
dodecahedrons
This next shape is a little easier to make, but still rather hard. It’s
made out of pentagons, and it’s called a dodecahedron (doh deh kuh
[hee]{.smallcaps} druhn) —a solid shape with twelve sides.
The ancient Greeks who discovered how to make these shapes called them
regular solids. A regular solid is a shape with an even number of sides
that are all the same size and shape.
There are many other solid shapes that can be made out of flat shapes.
But most of these solid shapes have an unequal number of sides or
differently shaped sides. For example, the pyramids built by the
Egyptians have five sides. Four of the sides are triangles, but the
fifth side, the bottom, is a square.
You might find it fun to see just how many different kinds of solid
shapes you can make out of flat ones. It’s actually possible to make any
kind of solid shape out of a flat one—even a ball! If you don’t think
so, look at a baseball. You’ll see that two flat pieces of leather, cut
to a special shape, were sewn together to cover the round ball!
Balls are solid shapes that can be made from such flat shapes as ovals
and hexagons, as you can see from these balls.
The Transamerica building in San Francisco is a pyramid. Each side is
a triangle and the bottom is a square.
Use the patterns in this book to make your own Christmas tree ornaments.
Cubes, pyramids, and other shapes can be made of colored or painted
paper. You can paint designs on them, glue on beads, and decorate them
in many ways.
