Grade 8 Math
posted by Al .
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?

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
Respond to this Question
Similar Questions

MATH
If the corresponding angles of 2 polygons are congruent and the lengths of the corresponding sides of the polygons are proportional, the polygons are... a. Regular b. Congruent. c. Symmetric d. Similar 
Please help Math
If the corressponding angles of 2 polygons are congruent and the lengths of the corresponding sides of the polygons are proportional the polygons are.. a. Regular b. Congruent c. Symmetrix d. Similar 
8th grade math
The total number of interior angles in two regular polygons is 17, and the total number of diagonals is 53. How many sides does each polygon have? 
Language Arts Help!!!!!
Identify two regular and two irregular polygons in your home or community. How do you know they are regular or irregular? 
MATHS
IF ONE OF THE INTERIOR ANGLES OF A REGULAR POLYGON IS TO BE EQUAL TO (9/8) TIMES OF ONE OF THE INTERIOR ANGLES OF A REGULAR HEXAGON,THEN THE INTERIOR SIDES OF THE POLYGONS IS .......? 
algebra
julia is studying the sum of interior angles in polygons. she creates polygons with 3,5,6,7 and 9 sides, and records the sum of the interior angles in each polygon in the table. Write an equation or inequality that represents the situation. 
maths
Ratio between number of sides of two regular polygons is 2:3 and ratio between degree measure of their interior angles is 3:4. Write the name of these polygons. 
math
Identify two regular and two irregular polygons in your home or community. How do you know they are regular or irregular? 
Math Help Please ASAP
I need someone to write this out for me like in a discussion so I can read it and write it in my own words please ASAP! Identify two regular and two irregular polygons in your home or community. How do you know they are regular or … 
math(Help me plz)
Identify two regular and two irregular polygons in your home or community. How do you know they are regular or irregular?