Posted by **Al** on Tuesday, June 2, 2009 at 7:58pm.

How can you use the measures of the interior angles of regular polygons to show that a platonic solid cannot be made from regular polygons that have more than five sides?

- Grade 8 Math -
**MathMate**, Tuesday, June 2, 2009 at 10:38pm
A platonic solid is a regular tetrahedron where all faces, sides and angles are congruent.

To create a solid, there must be at least three faces that meet at a vertex, which limits the interior angle of each face (polygon) to be **less than** 120 degrees. (At 120 degrees, the solid is a plane that contains no volume). The regular polygon with the most number of sides that satisfies this criterion is the pentagon, with an interior angle of 108 degrees (<120).

For more information and interesting reading, see:

http://en.wikipedia.org/wiki/Platonic_solid

## Answer this Question

## Related Questions

- MATHS - IF ONE OF THE INTERIOR ANGLES OF A REGULAR POLYGON IS TO BE EQUAL TO (9/...
- Please help Math - If the corressponding angles of 2 polygons are congruent and ...
- 8th grade math - The total number of interior angles in two regular polygons is ...
- MATH - If the corresponding angles of 2 polygons are congruent and the lengths ...
- algebra - julia is studying the sum of interior angles in polygons. she creates ...
- Language Arts Help!!!!! - Identify two regular and two irregular polygons in ...
- GEOMETRY - is it true that the sides of regular polyhedron although having to be...
- Math - Each exterior angle of a regular polygon is 15 degrees. How many sides ...
- Algebra - What is the measure of each of the interior angles of these regular ...
- geometry - I'm having trouble with an assignment that asks me to design a ...