Dodeca Hedron

Geometry Level 2

If you slice a dodecahedron in half parallel to two opposite faces, how many sides will the cross sectional area have?


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1 solution

Geoff Pilling
Apr 15, 2016

The only two faces that don't fall victim to "the slice" are the top and the bottom ones, leaving 10 faces that get sliced with the resulting cross section forming a regular decagon.

Can the same be generalised for any polyhedron with flat faces having e regular edges, which being cut half parallel to two faces yields a shape with 2e regular sides?

Silver Vice - 5 years, 1 month ago

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I don't think so, since for an icosahedron, with triangles, its, 12, or 4e... But I wonder if there is some generalization you can make with an equation based on its number of vertices, edges and faces...

Geoff Pilling - 5 years, 1 month ago

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I will work on it, try to list up values upto a finite value and try to find a pattern. The essence of such questions is to test the conjuration power of the brain, Being lazy I did it with a help of a rotating dodecahedron ;)

Silver Vice - 5 years, 1 month ago

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