Slicing an icosahedron
Geometry
Level
3
An icosahedron is carefully balanced on one of its vertices and then sliced horizontally through its center (half way between opposite vertices). How many sides does the resulting cross sectional area have?
Try more questions on Platonic Solids .
The answer is 10.
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1 solution
When an icosahedron is "standing" on one of its vertices, its 20 faces are oriented with 5 on the top (joined at the top vertex), 5 on the bottom (joined at the bottom vertex), and 10 around the side. These 10 around the side form the 10 sides of a decagon.