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All Five Platonic Solids - Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron
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Platonic Solids

What you will make:

In this project, learn a simple technique based on circles for making all five Platonic solids—tetrahedron, octahedron, icosahedron, cube, and dodecahedron. Each solid is made from a circle, with the shape the solid is based on drawn inside of the circle. This construction technique reinforces the concepts of Platonic solids as the student assembles each solid.

Circles with inscribed square, triangle or pentagon

Three-dimensional objects with only flat (or plane) surfaces are known as polyhedra. There are many different polyhedra, but five of them have the property of being regular, or "Platonic". A solid is regular if all planes (or faces) are the same, and the same number of planes meet at each corner (or vertex). Five solids qualify as regular: three are based on equilateral triangles (tetrahedron, octahedron, and icosahedron), one is based on squares (cube), and one is based on regular pentagons (dodecahedron).

For other geometric solids to make, see the project Geometric Solids.

Here's what you need:
  • Computer paper or cardstock, plain or colored
  • Optional: Empty ballpoint pen and ruler, markers, crayons, stickers.
  • Glue or double-sided tape
  • Scissors

This project is rated EASY to do.

How to Make Platonic Solids

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

Choose the platonic solid you want to make—there are templates for triangle, square and pentagon faces. For the cube, print squares; for the dodecahedron, print pentagons, and print triangles for the tetrahedron, octahedron and icosahedron (2 sheets). Download and print the pattern on paper or cardstock. The patterns are available in color or in black and white, for you to print on colored paper or add your own design. There are also pentagon patterns for making dodecahedron calendars for 2012, 2013 and 2014.

Triangles
Printable pattern for triangles to make tetrahedron, octahedron or icosahedron
Squares
Printable pattern of squares for making a cube
Pentagons
Printable pattern of pentagons for making a dodecahedron
2014 Calendar
Printable pattern of pentagons for making a dodecahedron calendar 2014
2013 Calendar
Printable pattern of pentagons for making a dodecahedron calendar
2012 Calendar
Printable pattern of pentagons for making a dodecahedron calendar

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: Cut Circles
Platonic solids - cut circles

Cut on the outline of each circle.

  • Tetrahedron - Cut four circles with equilateral triangles.
  • Cube - Cut six circles with squares.
  • Octahedron - Cut eight circles with equilateral triangles.
  • Icosahedron - Cut twenty circles with equilateral triangles.
  • Dodecahedron - Cut twelve circles with pentagons.
Step 3: Fold Platonic solids - fold sides

Fold on each of the three (or four or five) fold lines. To hide the printed fold lines, turn the circle with the printed side down before folding; otherwise, keep the printed side up. Repeat for each circle. For circles printed on cardstock, score the fold lines first with the empty ballpoint pen.

You may optionally decorate the inner triangles, squares, or pentagons with crayons, markers, stickers, or rubber stamps. Decorate on the unprinted side.

Step 4: Glue Parts

When gluing, use the folded sides as glue tabs, and keep them on the outside.

Platonic solids - glue parts together
  • Tetrahedron - Glue three folded circles with triangles together to form a pyramid. Glue them so that they meet at one point. One circle remains -- go on to Step 6.
  • Cube - Glue three folded circles with squares together to form one corner of the cube. Glue them so that they meet at one point. Repeat for the other three circles. To finish assembling -- go on to Step 6.
  • Octahedron - Glue four folded circles with triangles together to form a pyramid shape. Glue them so that they meet at one point. Repeat for the other four circles. To finish assembling -- go on to Step 6.
  • Dodecahedron - Glue five folded circles with pentagons around the sides of a sixth. Glue the sides together to form the top. Be sure that the glue tabs are on the outside. Repeat for the bottom. To finish assembling -- go on to Step 6.
  • Icosahedron - Glue five folded circles with triangles together to form the top. Glue them so that they meet at one point. Repeat to form the bottom.
Step 5: Make Ring Platonic solids - make ring for icosahedron

Icosahedron only: Glue ten folded circles with triangles into a ring using the glue tabs.

Step 6: Assemble

Glue the parts together.

Five platonic solids
  • Tetrahedron - Complete the shape by gluing the last circle into the bottom of the three-sided pyramid shape.
  • Cube - Glue the two pieces together.
  • Octahedron - Glue the two four-sided pyramid shapes together at their bases.
  • Dodecahedron - Glue the top and bottom together.
  • Platonic solids - assembling icosahedronIcosahedron - Glue the top to the ring, then glue the bottom to the ring.

Tip: If you want, the glue tabs can be folded down and glued to a face or trimmed to one-eighth of an inch.

That's it! Your Platonic solids are complete!
All Five Platonic Solids - Tetrahedron, Cube, Octahedron, Dodecahedron, 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!!!

Dodecahedron calendars - 2014

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Tip: Make a calendar in the form of a dodecahedron. Print the 2014 calendar pattern on paper or cardstock and assemble following the instructions in this project. For more creativity, you might print the black & white 2014 calendar pattern on white or pastel colored cardstock and decorate it with markers in any way you like!

Cube - tabs glued inside

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Tip: Glue tabs can be glued inside for a neat look.

Octahedron with stars

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Tip: These solids can be used as gift boxes. Print directly on cardstock. Decide how you want the box to open and leave tabs unglued as needed for a lid.

Dodecahedron - half of solid used as bowl

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Tip: The bottom halves of the dodecahedron and icosahedron can be used as bowls for party decorations. Pictured: the bottom of the dodecahedron filled with paper flowers attached to a balloon.

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