Polygons from a dodecahedron
How many different types of regular polygons can you get from the cross section of a dodecahedron?
For example, if you can make 20 squares and 16 equilateral triangles, and no other regular polygons, your answer would be 2 for the two different shapes.
Clarification : A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
Try more questions on Platonic Solids .
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1 solution
You can make an equilateral triangle by slicing off a vertex at equal distances along the edges that meet at that vertex. You can make a square by slicing off an edge and including all four edges that connect to that edge in their entirety. You can make a regular pentagon by cutting off a face (cutting parallel to the face) without cutting off any vertices other than the vertices on that face. You can get a regular hexagon by slicing right through the middle between opposite vertices. And, you can create a decagon by slicing right through the middle between opposite faces.
So that's 5 in total - 3, 4, 5, 6 and 10 sides