Polyhedron Project
A. What polyhedron (-hedra) did you pick?
B. How many sides does this polyhedron have?
C. What polygons are used to make this polyhedron? How many of each?
If you have problems getting the answers to Band C from our poster, you might
want to visit:
http://www.mathconsult.ch/showroom/unipoly/list-graph.html
http://www.uwgb.edu/dutchs/symmetIy/polydata.htm
http://www.ScienceU.com/geometry/facts/solids/handson.html
http://mathworld.wolfram.com/topics/ArchimedeanSolids .html
Your assignment (for 75pts) is to construct at home the semi-regular polyhedron(­
hedra) you picked. Your grade will be based on the quality of your project
including the element of color (don't make your's completely white or "manila"
colored) the accuracy of your joinery, and correctly calculating the surface area of
your polyhedron.
You will need the following: Poster board (thicker is better, at least 2 sheets, more
depending on the size you choose for each side.), Heavy duty tape (not scotch),
and something to cut with (utility knife or razor and straightedge. Make sure you
put something down to protect the surface you cut on! This will cause your
parents to continue to love you and not chase you with sticks.)
1. Construct your own templates. Yes, that's right, construct. You should be able
to do constructions for equilateral triangle, square, and hexagon. I will offer a
tutorial session for the pentagon during lunch on
. You will need all of
lunch period (so brown bag it that day if you need). For this presentation, you
must bring your compass, protractor and straightedge. Remember, all the sides
and angles in a regular polygon must be congruent. Measure each angle when
you are done to make sure they are all the same before you move onto step 2
IMPORTANT: The minimum side length is either 4 or 5 inches depending on the
polyhedron/ -ra you must make. If there is no number stated, it is assumed to be
4". Also don't make the sides any longer than 6". This will ensure that you can get
your polyhedron inside the classroom. You can use longer sides if you want to
build your polyhedron inside the class. VERY IMPORTANT: I've given you these
measurements that fit through the school doors, not the doors of your family's car!
Plan ahead if you're building a big one and need to arrange alternate
transportation."
2. Now trace your template polygons on the poster board. You will nEL(
1n
this a number of times. How many times? As many times to make 11 I ::-!d ',,> In
your polyhedron that have that face. Be careful with this tracing; 1"11 _ . l i n
carefully you trace, the easier it will be to assemble your polyhedrull<
3. Next, cut each of these polygons out. Be careful! Once again, the more
accurately you do this step, the more accurate your polyhedron will be. You
might want to use a utility knife and straightedge to get perfectly straight sides"
4. Now, tape all your polygons together to form your polyhedron. Make sun:~
you tape the edges together from the inside. Don't rush, or your pr,oject will
look messy and slip shod. Make sure you run tape the whole length of the side
you your project will suffer terrible gapping. It will be harder and harder to tape
the sides together (especially the last two or three) because your figure will b
mostly enclosed by then. Be patient. Apply tape to outside of polyhedron Ql4 . if
you must, and only on the last few edges. Don't use scotch tape, it's too wea
Use duct, brown or clear packing tape. Another technique is to add flaps to the
sides of the polygons and then use a glue gun to attach sides by gluing the flaps
together.
5. Finally, the write up. On a separate sheet of paper, tell which polyhedron or
polyhedra you made, what length sides you used, and how many pieces of
poster board you used for each. Find the surface area of your polyhedron.
Show your work. Make sure you show which general formulas you used and
tell why you used those. Finally write your name and the surface area on the
polyhedron (or on each of the polyhedra) you made.
This 75pt. (30 for surface area and write-up, 45 for construction, craft, and
joinery) project is due on
_
Extra Credit: Determine the volume in cubic inches of your project and show how
you arrived at that.