A polyhedron (many sided) is a three dimensional object that has four or more flat faces that are polygons (many edges). It is one of 13 different polyhedrons that can be built only with a combination of triangles, squares, pentagons, hexagons, and octagons. What makes at special is that of all 13, it has the most faces. The are 12 face pentagons, 60 edge triangles, and 20 corner triangles, for a total of 92 faces.
This Instructable includes a pdf for you to print the required pieces. The rest of the Instructable will show how to assemble it.
Also included is a SVG file if you care to laser cut your pieces.
Teachers! Did you use this instructable in your classroom?
Add a Teacher Note to share how you incorporated it into your lesson.
Step 1: Prep Your Pieces
You are going to need 80 tabbed triangles and 12 tabbed pentagons. The pattern has 20 and 3 respectfully so you will need to print four pages and cut them out. Then fold the tabs of all the pieces. (It is easier to fold in you score the fold lines.)
Step 2: Assemble 12 Stars
Each star uses one tabbed pentagon and five triangles. Assemble them with you glue of choice. I used.
Step 3: Assemble the First Three Stars
When assembling the stars you must always glue the left side of a point on a star to the left side of a point of the other star. If it isn't left on left you are doing something wrong. You may find it easier to mark the left side tabs, on the glue surface, with a pencil or marker.
Glue the 2nd star to the 1st star and the 3rd star to the 2nd star has shown in the 1st photo. This photo also points to how the 3rd star is glued to the 1st star. The 2nd photo shows what it looks like completed.
Step 4: Add on the Next Three Stars
Take the assembly from step 3 and place the next three stars as shown in the 1st photo. The 2nd photo shows them glued on, each by one tab. (remember left/left) Also there are arrows to show where they are next glued. Turn this assembly over. It should look like the 3rd photo.
You now have an assembly with six tabbed pentagons and ten tabbed triangles.
Step 5: Three More Stars Make Nine
With the assembly turned upside down, glue on the next three stars. Their position is fairly apparent but it is shown in the 1st photo. Again the left dots help a lot. The 2nd photo shows how it should look.
Step 6: Make the Top and Attach
Follow the directions in Step 3 to make the top. Now the top is ready to be attached. This would be a god time to place anything you what trapped inside. The 2nd photo shows it all closed up.
Step 7: You Can Stop Here If You Want
Presently you have a polyhedron with 12 pentagons face pieces, 60 triangles used for edge pieces, and 20 empty triangular spaces in the corners. However. it is stable and you can leave it this way if you wish. You have 20 tabbed triangle left. I used them to make an icosahedrons as shown in the photo.
The next one you make you could place the icosahedron inside the snub dodecahedron to make an interesting table piece. You can put anything in you want in it except soup. You could also wire the a snub dodecahedron with a small corded light and you have an interesting hanging architectural lighting fixture.
The diameter of the snub dodecahedron is roughly four time the length of the sides that make up the pentagons and triangles. So it would be very easy to size you patterns to what ever diameter you want.
Step 8: Fill in the Corners
I built the polyhedron this way to show the leaving the corners is an option. For the next and all another ones it is best to glue in the corners while assembling it. Anyway glue all 20 corners into place.
Before placing the last corner you may want to put something in it. Fill it with candy and you have a pinata. Again the diameter is roughly four times the edge length.
Make one the size you want and attach a cord to it and of have hanging decoration. Spray with glitter, glue on some small mirrors, and you a disco ball. In fact I saw some shiny silver colored poster board at the art store. I might just have to make one just as soon as I can find my old polyester bell bottom slacks.
Participated in the
Made with Math Contest