outer circumference of a CD-ROM disk mark 5 points, which are vertices of a
regular polygon of 5 sides. Two neighboring vertices create an angle 72 degrees
with respect to the center of disk.
With a compass mark 5 points with a supposed distance. You will see if a chosen distance is too small or too large. Shorten or enlarge this distance if needed and start marking with a compass again until good result is obtained.
Join with a ruler and a pen vertices to see a regular polygon of 5 sides. Cut with scissors along these sides. After this we should receive a piece of CD-ROM with a shape of regular polygon (of 5 sides).
Mark this polygon on other 11 CD-ROM disks and cut as before all 11 with scissors. After this we should receive 12 regular polygons formed from 12 circular CD-ROM disks.
Remark. Some people are using a hot knife to cut CD-ROM disks (or rather - to melt them along lines). ‘Literka’ doesn’t advise this method. This must be done when adult persons are present. This method is time consuming.
Take six of out of 12 polygons and place them on a table in the following way:
Fasten them with scotch and put them upside-down to have scotch on the bottom.
Pick up two outer polygons (blue ones), which are close to each other. Bend upward these two polygons until edges will touch each other. Fasten them with scotch.
Do the same with the all other outer polygons (blue ones). We should receive something like this (colors are changed):
Put some glue between edges of this polyhedron.
Do the same another copy of just obtained polyhedron. Use 6 CD-ROMs which are left and do the same as in step 2. Wait until glue is hardened.
Close two obtained polyhedrons placing them one on another. If there are some discrepancies and edges do not correctly touch each other, fix it with scotch. Then put some glue between edges.
Cover faces of a polyhedron with colored paper. Do it the way that each 2 faces with a common edge are covered with 2 different colors. Think about the smallest number of colors you can use.
Having done everything you can start solving the following problem:
Suppose you have 12 another copies of your construction. Hence these are also regular 12-faces polyhedrons with edges of the same length as in your polyhedron. Will it be possible to glue them to your polyhedron face-to-face?
In other words: glue each one of 12 copies to 12 faces of your polyhedron, one polyhedron to one face – is this possible?
Another explanation: Look at the picture of step 2. Five polygons are ‘glued’ to one polygon. You cannot do it with a regular octagon (regular polygon of 8 sides).
Notice: There is a special page of ‘Literka’ with pictures of all types of regular polyhedrons.
Notice: Terminology and some concepts of this page were taken from the handbook of H. Steinhaus ”Mathematical kaleidoscope” as well as from some Yahoo geometrical WebPages.
There is a page of 'Literka' about Volume of regular icosahedron.