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Similarities: both have a base which extends into a single vertex.

Differences: a cone only has 1 edge and a pyramid has a minimum of 6 (for a triangular pyramid).

the base of a pyramid is a polygon - the base of a cone is a curve

(a mathematical cone has no edges at all it is a continuous sheet - or two sheets if you consider the vertex as dividing the surface into two sheets).

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Q: Similarities and differences between cone and pyramid?
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