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


We can divide a regular icosahedron into 3 sections: a top section with 5 triangular faces, a middle section with 10 triangle faces and a bottom section with 5 triangular faces (note: the bottom section is a symmetry of the top section).

The top section of 5 triangular faces has 6 vertices: one from the concurrency of the 5 faces and the other 5 from bases of the triangles. Since the bottom section is a symmetry of the top section, the bottom section also has 6 vertices. All the vertices of the triangles that are in the middle section that connects the base of the top section and the base of the bottom section are already accounted for since they either form the base of the top section or the base of the bottom section.

Therefore, there are 6 + 6 = 12 vertices in a regular icosahedron.

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