math cats make a tetrahedron

make a tetrahedron!

Tetra- means four, and -hedron means base. Tetrahedrons have four bases (or faces).

1. Draw a circle.

2. Place your compass point on the edge of the first circle and draw another circle.

3. Place your compass point on an intersection and draw a third circle.

4. Draw line segments connecting all the intersections. (Use your straight edge. You can score the lines with a ballpoint pen.)

5. The four triangles will become the four faces of the tetrahedron. Mark three tabs with a T, as shown. (You'll use the tabs to glue the edges of the triangles together.) You will not need the shaded sections. Carefully cut out around the white area--the four triangles and three tabs.

Note: You may notice that you've used a whole sheet of paper to create a fairly small space form. If you want to make the largest possible tetrahedron out of one sheet of paper, you do not really need to draw three full circles on the paper. Open your compass wider and place it as shown so that your triangles and tabs still fit on the paper but unneeded portions of the circles get cut off.

6. After you have cut out your shape, fold carefully along each line. (If you draw your lines firmly with a ballpoint pen, that "scores" the paper so it is easier to fold. Also, it helps to lay your straight edge along the line as you are folding.) Fold the tabs down, too. Check to be sure that the point of one folded triangle meets up with the point of the triangle underneath it. Crease each fold with a fingernail or the side of a pen or pencil so that each fold is very crisp.

If you are going to decorate your space form, it is easier to do this before you glue it. (Be sure to decorate the blank side, not the messy side with all of the curves and lines.)

7. It's time to glue! Be sure that the tabs are glued to the inside of the triangles so they don't show. Glue one edge at a time. However, if you use rubber cement (outside, because the fumes are bad for you), there is an opposite trick for making a fast, strong bond: Put rubber cement on all of the tabs and on all of the edges which the tabs will be touching. Let all of the tabs and edges dry. Then stick the tabs to the edges. They'll hold tight, instantly.

8. There is always one triangle which has no tabs. That is the one you should glue last. And just before you glue it, tie a long loop of thread to a paper clip and insert the clip into the space form. When you glue the last face, the paper clip will be trapped inside the space form, and the thread will be all set for hanging the form.
Now your polyhedron is ready to hang!

introduction hexahedron octahedron decahedron icosahedron

1. Draw a circle.
	2. Place your compass point on the edge of the first circle and draw another circle.
3. Place your compass point on an intersection and draw a third circle.
	4. Draw line segments connecting all the intersections. (Use your straight edge. You can score the lines with a ballpoint pen.)
5. The four triangles will become the four faces of the tetrahedron. Mark three tabs with a T, as shown. (You'll use the tabs to glue the edges of the triangles together.) You will not need the shaded sections. Carefully cut out around the white area--the four triangles and three tabs.
	Note: You may notice that you've used a whole sheet of paper to create a fairly small space form. If you want to make the largest possible tetrahedron out of one sheet of paper, you do not really need to draw three full circles on the paper. Open your compass wider and place it as shown so that your triangles and tabs still fit on the paper but unneeded portions of the circles get cut off.
6. After you have cut out your shape, fold carefully along each line. (If you draw your lines firmly with a ballpoint pen, that "scores" the paper so it is easier to fold. Also, it helps to lay your straight edge along the line as you are folding.) Fold the tabs down, too. Check to be sure that the point of one folded triangle meets up with the point of the triangle underneath it. Crease each fold with a fingernail or the side of a pen or pencil so that each fold is very crisp.
	If you are going to decorate your space form, it is easier to do this before you glue it. (Be sure to decorate the blank side, not the messy side with all of the curves and lines.)