Math Is Fun Forum

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

[ASK] Volume of Icosahedron

I want to prove the formula of regular icosahedron's volume. The reference says that the volume is

. For this, I need to split the icosahedron to 20 triangular pyramid with the same size. I assumed that the base area is

and the pyramid's height is

(I assumed that the pyramid's height should be equal the distance from midpoints of A'B' to the center point of pentagon A'B'C'D'E'. However, no matter how hard I tried and changed the form, I was unable to reach the form

. Is the pyramid's height not equal the distance from midpoints of A'B' to the center point of pentagon A'B'C'D'E'? If so, how to determine their distance?

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: [ASK] Volume of Icosahedron

see Maths Teaching Resources.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob