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Is Euler's formula applicable on all polyhedrons? |
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Answer» Euler’s Formula does however only work for Polyhedra that follow certain rules. The rule is that the shape must not have any holes, and that it must not intersect itself. (Imagine taking two opposite faces on a shape and gluing them together at a particular point. This is not allowed.) It also cannot be made up of two pieces stuck together, such as two cubes stuck together by one vertex. If none of these rules are broken, then F+V-E=2 for all Polyhedra. Euler’s formula works for most of the common polyhedra which we have heard of. There are in fact shapes which produce a different answer to the sum F+V-E. The answer to the sum F+V-E is called the Euler Characteristic χ, and is often written F+V-E=χ . Some shapes can even have an Euler Characteristic which is negative! |
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