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Geometric Solids - Tetrahedron, Octahedron, Icosahedron
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Geometric Solids

What you will make:

In this project, make four of the five Platonic solids—cube, tetrahedron, octahedron, and icosahedron. The tetrahedron and cube are easy to make, while the icosahedron can be hard for children under ten. Make the tetrahedron before trying to make either of the other two solids.

These geometric models can be used for things beyond learning about solid geometry. Decorate them and make a colorful mobile with a paper plate and some string. Use them as Christmas tree decorations, or use one as a gift box and put a small present inside.

Related craft: For another way to make geometric solids, see the  Platonic Solids craft project. Believe it or not, each solid is made from circles!

Geometric solids are three-dimensional objects like spheres, cones, and cubes. Solids with only flat surfaces and straight lines are known as polyhedra. There are many different polyhedra, but five of them have the property of being "regular". A solid is regular if all of its faces are the same, and the same number of planes (faces) meet at each corner (vertex). Five solids qualify as regular (also known as Platonic)—three are based on triangles (tetrahedron, octahedron, and icosahedron), one is based on squares (cube), and one is based on regular pentagons (dodecahedron).

Three of the solids in this project are based on equilateral triangles. The tetrahedron has four sides (or faces), while the octahedron has eight and the icosahedron has twenty. The tetrahedron has three triangles that meet at each corner (or vertex). Four triangles meet at each corner of an octahedron, and five triangles meet at each corner of an icosahedron. Examine your models to see these properties.

Here's what you need:
  • Cardstock, plain or colored
  • Glue or double-sided tape
  • Scissors
  • Bone folder or empty ballpoint pen
  • Ruler

This project is rated EASY to AVERAGE to do.

How to Make Geometric Solids

Read all of the steps before starting.
Step 1: Choose a Pattern and Print It

Choose the geometric solid you want to make! There are templates for a cube, a tetrahedron, an octahedron and an icosahedron. Download and print the pattern.
Choose a design that prints in color, select a black & white pattern to print on colored cardstock, or use your creativity to decorate the solid.

Printable pattern for tetrahedron
Printable pattern for octahedron
Printable pattern for icosahedron
Printable pattern for cube
Printable pattern for tetrahedron with dots
Printable pattern for octahedron with dots
Printable pattern for icosahedron with dots
Printable pattern for cube with dots

Patterns are Adobe PDF files. The Adobe Reader is available for free.

All of Aunt Annie's project patterns are designed to be printed on standard letter-size paper (8.5"x11" or A4). When printing from Adobe Reader, you may need to select Auto-Rotate and Center or Choose paper source by PDF page size to ensure the best fit.

Step 2: Color Pattern (optional)

Color the pattern template as you like with markers, colored pencils or crayons. You don't need to color the glue tabs.

Step 3: Cut

Cut around the polyhedron's pattern on the outline. Try to make your cuts very straight and smooth. There will be one piece, ready to fold, after you cut. (The octahedron pattern and tetrahedron pattern have two templates—small and large.)

Step 4: Score Geometric solids - score fold line

Scoring the fold lines makes for easier folding and sharper creases. The fold lines are marked in blue on the illustration.

To score: Turn the template with the printed/decorated side up. Use a ruler and the empty ballpoint pen (or bone folder) to make an indent along the fold lines.

Step 5: Fold Geometric solids - fold

With the printed side down, fold each line that has been scored.

Be sure that all folds are sharp.

Step 6: Glue Geometric solids - glue

Gently form the solid into its shape, referring to the illustration on the pattern. Carefully glue each tab into place. The tabs can be glued on the outside where the sides meet, or on the inside. It is much easier to glue the tabs on the outside, but the solid will look neater with the tabs glued on the inside.

That's it! Your geometric solids are complete!
Geometric Solids - Tetrahedron, Octahedron, Icosahedron

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Before you start:
  • Make a place to work.
  • Read all of the directions.
  • Gather everything you need to do the project.
  • Think about the project. Imagine how it will look and what you will do with it.

Are you ready?
Okay, get started!!!

Octahedron - tabs glued inside

Tip: The octahedron patterns include two sizes. (So do the tetrahedron patterns.) Glue tabs can be glued inside for a neat look.

Tetrahedron - glue tabs on outside

Tip: This tetrahedron has the glue tabs glued on the outside for a different look. This is a much easier way to glue the solid models.

Gift boxes made from geometric solids patterns using ePaper

Project Extra: For a cute set of solids or a gift box, print these Polka Dot ePapers on cardstock with the solid's pattern on the reverse side.

Geometric soilds with dots

Tip: The solids made with the dotted patterns are cute and clearly show the triangular faces.

Icosahedron - tabs glued inside

Tip: The colored icosahedron model has five colors that meet at each vertex. The cube has three colors meeting at each corner.

Cube - tabs glued inside


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