Polyhedron Project

Due Dates: June 1st and 2nd

***2 Minor Grades***

Regular Polyhedra

We know that a regular polygon has congruent sides and angles.

A regular polyhedron has congruent sides, angles, and faces.

There are only 5 regular polyhedra.

Regular Polyhedra

Cube

Regular Polyhedra

Tetrahedron

Regular Polyhedra

Octahedron

Regular Polyhedra

Dodecahedron

Regular Polyhedra

Icosahedron

You will construct a regular polyhedron “ornament” for 2 minor grades. Here are the criteria:

1)Choose from

- Octahedron (extra credit only)

- Dodecahedron

- Icosahedron

Directions will follow on how to create these…

You will construct a regular polyhedron “ornament” for 2 minor grades. Here are the criteria:

2) Decide on a theme

Your finished product should be colored/decorated according to a theme of your choosing.

Examples: Sports, characters, Celebrities, your favorite things about Heritage High…

You will construct a regular polyhedron “ornament” for a major grade. Here are the criteria:

3) Can I earn bonus points??

Bonus points will be left to the discretion of the teacher.

You could possibly earn bonus points by creating more than one polyhedron and incorporating them into your ornament.

Or “Dice of the Gods”

Polyhedron Ornaments

To create the "Dice of the Gods", otherwise known as the five platonic solids: tetrahedron, octahedron, cube, icosahedron, and dodecahedron,

you will need:several greeting cards or pieces of colored card stock or even cereal box sides a compass for drawing circles a ball point pen a ruler or straightedge a pair of scissors a stapler or glue if you prefer

Draw a circle on the back of your card or cardstock etc. The size of the circle is up to you. The larger the circle, the larger each face of your "dice" or polyhedron.

You are going to need to inscribe an equilateral (all sides the same length) triangle inside the circle.

To do this, keep the compass locked open to the same radius you used above and draw a single starting point on the circle.

For a tetrahedron, For a tetrahedron, octahedron or octahedron or icosahedron…icosahedron…

Now with the compass point seated on that starting dot, use the compass to mark off equal increments around the circle.

Simply mark your way around the circle. You will eventually reach your original starting dot.

You will have six equally spaced marks.

Now connect every other mark with your straight edge and you will have created an inscribed equilateral triangle into the circle.*We will be using the circle pattern first, and then we will cut out the triangle and use it as a pattern.

Here we cut out the circle pattern. Be sure to keep the leftover frame. We will use it as a viewfinder to select the best spot to cut out of our cards.

It really helps to be able to move the viewfinder around and find the best place to draw the circle.

Lay your solid circle pattern over the spot you've selected and trace the circle.

Cut out the circle and you are on your way to a really cool 3-d figure.

You will need to cut out a circle for each face, or side, of the polyhedron you are making.

tetrahedron = 4 circles octahedron = 8 circles cube = 6 circles* icosahderon = 20 circles dodecahedron = 12 circles**

* The cube will need to have a square inscribed into each circle instead of a triangle.** The dodecahedron will need to have a regular pentagon inscribed into each circle.

You are going to need to inscribe a regular pentagon inside the circle.

Then connect the five points where each radius intersects the circle.

For a dodecahedronFor a dodecahedron

Now it is time to cut out the triangle pattern. (or square or pentagon)

To create the flaps for connecting our figure, we will be tracing the triangle pattern onto the back of each circle.

RED ALERT: this step is vital!Be sure to use your straight edge and the ball point pen to go over very firmly each side of this triangle you just traced. This is known as "scoring" and it will give you a perfect fold, because the pressure of the pen starts the crease of your fold.

All you will need to do is lightly press the scored flaps up.*NOTE: if you fold them up as in this demonstration, your polyhedron will be quite decorative with the flaps showing on the outside.

If you would rather have a smooth outer skin with no flaps showing, we recommend folding them down and using glue to attach the flaps.

We always check the back for proper alignment before we glue.

We are going to make the above icosahedron. So start gluing the flaps. If you want a firmer, more rigid bond, we recommend white glue. Remember however that this will greatly increase your construction time, as you will have to wait for the glue to dry.

Here you see five triangles stapled together into a pentagonal "top" of our icosahedron.

Do the same for the bottom.

Here is an underside view. We are now ready to make the middle with the remaining 10 triangles.

Glue the remaining triangles together like this.

Here is what it looks like with the bottom connected to the middle. All it needs is the top to finish it off!

Here is the finished product!

The famous dodecahedron.

The icosahedron.

The octahedron.

The cube, sometimes called a "hexahedron".

The tetrahedron or "regular pyramid".