The solid figure having eight vertices is the hexahedron. A cube, which has six faces (classifying it as a hexahedron) as well as the eight vertices, is a regular hexahedron. It is doubtless the best example of this category of geometric shapes. A link can be found below for more information, and some drawings to really help lock in the idea.
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A quadrilateral based pyramid.
A hexahedron is a solid figure with 6 plane faces (which is where the prefix hexa- comes from), eight vertices and 12 edges.
Heptagonal prism
sphere
A square pyramid.