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Q: What shape has one vertex and one edge?

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A cone has one vertex and one edge.

A cone has one vertex, one edge, and one base.

A lenticular shape: the shape of a lens.

How about a sphere as an example that fits the given description

Conventionally, two faces, one edge and one vertex.

A cone would fit the given description.

circle

The Cone

Two faces, one vertex and one edge on a finite cone.

L shape

A finite cone has one vertex (not vertices!), 1 edge and 2 faces.

A cone.

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