Polyhedron Ornament Project
Purpose: The student will use basic geometry construction techniques to construct an icosahedron, which is a polyhedron with 20 faces.
Materials needed: compass
straightedge/ruler
scissors
glue (hot glue works well)
yarn, ribbon, or string
card stock, poster board, or Christmas cards
(Construction paper will not work.)
Procedure:
Using the illustration on the back of this sheet as a guide, use a compass to construct twenty congruent circles on the card stock, poster board, or Christmas cards.
Keeping the compass open to the distance of the circle’s radius, make six arcs around the edge of each circle. Connect every other arc using your straightedge to form an equilateral triangle that is inscribed within the circle. Do this for all 20 circles and cut them out with the scissors.
Fold the circular flaps up or down, depending on how you want it to look, along the sides of the triangle. These flaps are called segments of the circle. Pressing along the fold with your scissors or a pencil will result in a sharper crease.
Apply glue to the back of one flap of two triangles and join to start forming the middle band. Continue gluing triangles together until ten triangles are assembled as shown. Join flap A to flap A. This will close the middle band.
Glue five triangles together at the flaps to make the top. Now is a good time to put a hanger in the top. Glue the unmarked flaps together. This will make the top pop up. Repeat this process to form the bottom.
Join the top to the middle band by gluing flaps B to B, C to C, etc.
Join the bottom to the middle band.
Finish by applying the glue to the edges of flaps and decorating as you wish. DO NOT USE SPRAY PAINT !! Be creative. This project should be acceptable to display at school. Answer the questions on the back regarding your project.
Grade: This project is a test grade. Penalties will be applied for late projects.
Assigned date: November 16-17Due date: December 2
CATEGORY / 4points / 2points / 0pointsFollow directions / Student used glue and included a hanger, student's name is on the project, card stock was used, AND no spray paint was used. / Missing 2-3 of the items listed to the left. / Missing 4 or 5 of the items
Listed.
Questions on back / Missed 0-1 problem / Missed 2-4 problems / Missed 5 or more
Quality / Project is neat; student put in effort; creativity was shown. / Project is messy OR no effort and no creativity was shown. / Project is of such
low quality,
it falls apart.
Mechanics-20 circles/equil. triangles / 20 circles were used and equilateral triangles are visible. / 20 circles were not used OR a compass was obviously not used to create equilateral triangles. / 20 circles are not
included AND a
compass was not used.
Mechanics-spherical/correct / The product is spherical in shape and it is put together correctly with no holes or gaps. / The product is not spherical OR it is not put together correctly shown by evident holes and gaps. / The product is not
spherical AND it is
not put together
correctly shown by
evident holes and gaps.
Points GradePoints Grade
2010010 75
1895 8 70
1690 6 65
1485 4 60
1280 2 55
Answer these questions and return this sheet with your project !
1. What is the radius in cm. of each of the circles you used in your
project? ______
2. What is the area of all 20 of your circles combined? (A = πr2)
______
3. Suppose the project was made with the flaps inside, describe what
you would need to do to find the surface area of the finished product.
______
______
______
4. Classify the inscribed triangle by angles and by sides.
______, ______
5. How many arcs did you need to make on each circle ? ______
6. Since a circle is 360º around, how many degrees are in each section
that was made by the arcs you drew? ______
(Hint: 360 ÷ # of arcs)
7. Make a conjecture about the relationship between the angle measures
In the triangle from #4 and the degree measurement you found in
#6.
______
______
______
______
Refer to page 669 in your book to answer the remaining problems:
8. Regular polygons are also called
______.
9. Name the five regular polyhedrons along with their number of faces.
Name / # of faces