A geodesic dome, or geodome, is a set of polygons that are organized together to form a half sphere or dome. This fun project teaches children about shapes, particularly about triangles and pentagons. You will learn how to draw a pentagon any size you want with a protractor and a ruler. Adult participation is required when cutting the cardboard pieces out.
Things You'll Need
 Large pieces of cardboard, plus extra scrap cardboard for padding when cutting
 Scissors
 Box cutter (adult required)
 Pencil
 Ruler
 Tape measure
 Duct tape
 Protractor

Once you have all the materials you need, decide how large you want your pentagons to be. You will need to cut out 6 pentagons and 10 smaller equilateral triangles. Using the amount of cardboard you have, estimate 6 square blocks of the same size that will be used to cut the pentagons. You'll also need some extra cardboard for for the ten smaller triangles, an additional 23 square blocks is enough for your triangles, depending upon how you cut out your triangles. Try to plan your shapes on the cardboard such that any folds in the cardboard are avoided. The folds will weaken the structure. Once you have gathered all your materials, begin calculating the size of your shapes.

Measure the length of the square blocks that you have reserved for creating the pentagons. The length of each side of the pentagon should be .58333 times the length of your block. For example, if the block is 3'x3', or 36"x36", the length of each pentagon side will be 1.75' or 21". Write down the length of the sides of your pentagon.
A pentagon is a 5 sided polygon where all sides are the same length and all five internal angles are 108 degrees.

Draw the first side of the pentagon centered at the bottom of the block. Use a protractor to measure 108 degrees from the left edge of the first line and draw a line the same length. Repeat this for drawing all sides of the pentagon.

An adult can then cut out the pentagon by using a box cutter (recommended) with extra scrap cardboard padding underneath so the lower surface doesn't get scratched, or use a strong pair of scissors. Then trace the pentagon onto the other five blocks and cut the pieces out.

Use the same length you used for the pentagon sides to make the ten equilateral triangles. An equilateral triangle has three equal sides and three internal angles of 60 degrees. An adult can cut out the triangles using a box cutter (recommended) with extra scrap cardboard padding underneath. The first cutout triangle can be used to trace the remaining triangles.

Once you have all 6 pentagons and 10 triangles cut out, assemble the pieces into a dome shape using duct tape. Follow the pattern in the picture to assemble the geodesic dome. Start by assembling pentagons and triangles around in a circle, leaving the top pentagon for the last piece. One triangle can be used for a door and should only be attached on one side so it can open and close. Alternatively, a pentagon can be used for a door and should only be attached on one side so it can open and close. A pentagon door is a larger door, but the structure will not be as strong. The duct tape allows for some flexibility and room for error if the pieces are not cut to exact specifications. One or both sides of cardboard can be duct taped together.

This is an upsidedown view of the geodome. It is included here to show you how to assemble the pentagons and triangles.
Tips & Warnings
 Our dome was built with pentagon sides that were 16 inches long. The dome is about 24 inches tall and 48 inches wide. Another variation includes building two domes together to make a geodesic sphere. Small or large domes can be made from these directions.
 Our geodome has been played with by many kids that come over to play. They enjoy hiding inside it, peeking out of it, and moving around like a large turtle.
 Adult supervision is required when building this dome. Box cutters are not for use by children.