A Polyhedral Demonstration of the Fact That Twenty Times Four Is Eighty

20 times 4 is 80

The Platonic solid known as the icosahedron has twenty triangular faces. This polyhedron resembles the icosahedron, but with each of the icosahedron’s triangles replaced by a panel of four faces:  three isosceles trapezoids surrounding a central triangle. Since (20)(4) = 80, it is possible to know that this polyhedron has eighty faces — without actually counting them.

To let you see the interior structure of this figure, I next rendered its triangular faces invisible, to form “windows,” and then, just for fun, put the remaining figure in “rainbow color mode.”

20 times 4 is 80 version twoI perform these manipulations of polyhedra using software called Stella 4d. If you’d like to try this program for yourself, the website to visit for a free trial download is http://www.software3d.com/Stella.php.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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