How Many Triangles in a Great Icosahedron?

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Icosahedrons are a shape in three dimensions that resembles a dodecahedron in many way. Find out how many triangles are in a great icosahedron with help from an experienced mathematics educator in this free video clip.

Part of the Video Series: Math Lessons
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Video Transcript

Hello, my name is Walter Unglaub, and this is how many triangles in a great icosahedron. So an icosahedron is a bit complicated to draw on the board. However you can think of the shape in three dimensions as a somewhat of a squashed dodecahedron covered on the surfaces by a set of 12 pentagramic pyramids. So a pentagramic pyramid would look from one side like this where you would have two sides, two faces on the other side of this pyramid and each face of this pentagramic pyramid actually has three triangles in it. So we simply count up how many total triangles there are in one pentagramic pyramid by counting the number of triangles on one face and multiplying that by five so we have one, two, three triangles and this is one side and because it's the pentagramic pyramid the base is a pentagon which means that there are five sides. So five sides or faces times three triangles is equal to 15 triangles. Now for a great icosahedron, there are 12 of these on the surface of the entire object. So all we have to do is multiply 12 with 15. Where 15 denotes the number of triangles per pentagramic pyramid and 12 is the total number of pyramids in the figure. And this is equal to 180 triangles. So this is how many triangles there are on the surface of a great icosahedron. My name is Walter Unglaub and this is how many triangles are there in a great icosahedron.


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