cone
A cone has one vertex, one edge, and one base.
A cone.
When a square pyramid is sliced perpendicular to its base through a vertex, the cross section will be a triangle. This triangle will have one vertex at the apex of the pyramid and the other two vertices on the base, forming a triangular shape that includes one of the pyramid's edges and a segment of the base. The resulting triangle will be isosceles if the slice is made symmetrically.
The solid shape you are describing is called a cone. A cone has a circular base and narrows to a single vertex, or apex, at the top. Its curved surface connects the base to the vertex, distinguishing it from other solid shapes.
A right truncated cone.
It's a pentagonal pyramid.
A right cylindrical cone has a circle for a base and one vertex. a diagram is shown on unitmath.com
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L shape
pyramid and coneIn the list given, only the cone and pyramid have a vertex.
A cone would fit the given description.
A diagonal in a shape is a straight line from one vertex to another vertex (corner).