Regular Polygon...
vertex
The apex is located above the centre of the base.
pyramid and coneIn the list given, only the cone and pyramid have a vertex.
The slant height of a square pyramid is always perpendicular to the base. It is form the top vertex all the way down to the most center of one side of the base edge.
A pyramid has a polygonal base with all other sides being triangles. As the Egyptians famously demonstrated, a common pyramid has a square base with four triangles meeting at a vertex, but any polygon - regular or irregular - can be used as the base of such a polyhedron.
A regular pyramid has a regular polygon base and a vertex over the center of the base. By:Cherrylvr :)
regular pyramid
vertex
Yes.
Yes
The distance from the vertex of a regular pyramid to the midpoint of an edge of the base can be found using the Pythagorean theorem. If the height of the pyramid is ( h ) and the distance from the center of the base to the midpoint of an edge is ( d ), then the distance ( D ) from the vertex to the midpoint of the edge is given by ( D = \sqrt{h^2 + d^2} ). This applies to regular pyramids where the base is a regular polygon. The specific values of ( h ) and ( d ) depend on the dimensions of the pyramid and its base.
A regular pyramid has an equilateral triangle base, not just a regular polygon. It has an apex above the centre of the base.
Vertex
In general, an octagonal pyramid is a pyramid with an octagon for a base and triangles (which all have a common vertex) for sides. The octagon my or may not be a regular one.
The apex.
The apex is located above the centre of the base.
pyramid and coneIn the list given, only the cone and pyramid have a vertex.