This portfolio assignment is to build a number of 3D models of polyhedra. The purpose is several-fold.
The assignment has a few parts. (1) The Basic Set (2) The Extended Set (3) Extras
Parts (1) and (2) are required parts of the assignment. Part (3) is for extra credit for those who really like to build models or for those who really like extra credit.
In addition to the models, you will write a Model Log. This is not too long, but it will contain the answers to some questions you are asked about the models and/or some drawings of nets.
Please read the Directions and Tips at the end for building the models.
Construct a model of a cubical box with edge length 4 inches. (You should leave one face hinged so that it will open.)
Construct a model of a regular tetrahedron that fits exactly in the cubical box from M1 so that the 4 vertices of the tetrahedron are exactly at 4 of the 8 vertices of the box. (Write in your log for M2 what is the edge length of the tetrahedron and why.)
Construct a regular octahedron so that the distance between opposite vertices (i.e., the long diameter) equals 4 inches. (Write in your log for M3 the edge length of the octahedron and show your reasoning.)
Construct a pyramid with a square base ABCD and a vertex E directly above one of the vertices A of the square. Make the edge length of the square = 2 inches and also the height AE = 2 inches. (The net for such a pyramid is #29 of Construction Portfolio 4.))
Construct a pyramid with a square base ABCD and a vertex F directly above the center O of the square. Make the edge length of the square = 2 inches and also the height FO = 2 inches. (A net for such a pyramid is #30 of Construction Portfolio 4.)
Construct a pentagonal anti-prism with a regular pentagon as base and equilateral triangles as side faces. (Write in your log for M6 a definition of an anti-prism. Cite your source.
For Part 2, find the definition of an Archimedean solid (polyhedron) and find some examples. Then make models of two Archimedean solids.
(Write in your log for M7 and M8 the definition of a regular polyhedron and also the definition of an Archimedean polyhedron, as well as the names of your models and a listing of the number of faces of each kind.)
Make one or two additional models. Give the name of each.
Since this is a geometry class, it is most important that the models be made accurately and are crafted well enough that they do give a good picture of the actual shape in space.
Materials: Make the models accurately of cardboard at least as heavy as a manila folder (Folders are good. Art board is good. Corrugated is too thick to be accurate for small models like these; notebook paper or construction paper is too flimsy). Tape the edges neatly. (Outside works best and a tape like Scotch transparent tape or packaging tape works better than Magic Tape or masking tape).
Hint: If you have a net printed or drawn on paper, you can transfer it to cardboard by laying the paper on the cardboard and pricking a hole in the paper at each vertex with your compass. Once you have the vertices poked through, you can remove the paper and draw in the line segments for the net on the cardboard.
Grading: Sign your work! Put your initials on each of your models. (You can make them small so that they are not defaced.) The models will be graded on (1) whether they are accurate, neat, hold together and are made of materials that work as well as the ones mentioned here (2) some additional credit for particularly fine craftsmanship or artistry, especially for the Extended Set or the Extras. The plan is that we will photograph the models as a record. We plan to use some of the basic models in 444 class on Wednesday, so timeliness is important. Some of the photos may end up taken during lab if time is short in the morning.
There is a very little bit about Platonic solids in BG, but you will need to go on the web for information, names, etc. There are 3D interactive Java models that you can rotate, but also some nice polygons and nets that you can print out to use. Some sample links are given on the Math 444 web site, but you can find a lifetime supply of sources if you use Google.