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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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New post 13 Feb 2017, 02:35
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Question Stats:

60% (01:43) correct 40% (01:34) wrong based on 82 sessions

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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

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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, 11:38
1
#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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New post 13 Feb 2017, 17:07
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Top Contributor
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, 12:50
2
My 2 cents:
It really helps to be able to imagine the diagram of icosahedron -
Attachments

icosehedron.png
icosehedron.png [ 25.53 KiB | Viewed 1308 times ]

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

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New post 23 Jan 2019, 13:27
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Re: A regular icosahedron is a three-dimensional solid composed of twenty   [#permalink] 23 Jan 2019, 13:27
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