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A regular icosahedron is a three-dimensional solid composed of twenty

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A regular icosahedron is a three-dimensional solid composed of twenty [#permalink]

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A regular icosahedron is a three-dimensional solid composed of twenty equilateral triangular faces, with five faces meeting at each vertex. How many vertices does a regular icosahedron have?

A. 5
B. 12
C. 20
D. 33
E. 60
[Reveal] Spoiler: OA

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Re: A regular icosahedron is a three-dimensional solid composed of twenty [#permalink]

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New post 13 Feb 2017, 12:38
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#of triangular vertices is 20*3=60

5 vertices/per icosahedron so 60/5=12.

B.

Not really sure though..
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Re: A regular icosahedron is a three-dimensional solid composed of twenty [#permalink]

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Bunuel wrote:
A regular icosahedron is a three-dimensional solid composed of twenty equilateral triangular faces, with five faces meeting at each vertex. How many vertices does a regular icosahedron have?

A. 5
B. 12
C. 20
D. 33
E. 60


Each triangle has 3 vertices, and there are 20 triangles in total.
So, the total number of triangle vertices = 3 x 20 = 60

Each vertex in the icosahedron is comprised of five triangle faces meeting at a point.
In other words, it takes 5 triangle vertices to make 1 icosahedron vertex .
We have 60 triangle vertices, so the TOTAL number of icosahedron vertices = 60/5 = 12

Answer: B

Cheers,
Brent
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A regular icosahedron is a three-dimensional solid composed of twenty [#permalink]

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New post 22 Feb 2017, 13:50
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My 2 cents:
It really helps to be able to imagine the diagram of icosahedron -
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A regular icosahedron is a three-dimensional solid composed of twenty   [#permalink] 22 Feb 2017, 13:50
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