A sphere has 0 vertices.
Understanding Vertices
A vertex, in the context of geometry, is a point where two or more lines or edges meet. This concept is straightforward for polyhedra (3D shapes with flat faces), where vertices are corners. However, a sphere is a curved shape and lacks these flat edges and corners.
Sphere Characteristics
- Curved Surface: A sphere is defined by a continuous curved surface where every point is equidistant from the center.
- No Edges: Unlike polyhedra like cubes or pyramids, a sphere doesn't have straight edges.
- No Corners: Similarly, because it has no edges, a sphere also has no distinct corners.
Why No Vertices?
The definition of a vertex requires the intersection of straight lines or edges. Since a sphere doesn't have any straight lines or edges, it cannot possess any vertices. According to reference material, a sphere has 0 edges and therefore, no corners formed by intersecting edges.
Summary
To reiterate, based on the fundamental geometric properties and the absence of edges and corners, a sphere has zero vertices.
| Feature | Sphere | Cube | Pyramid |
|---|---|---|---|
| Vertices | 0 | 8 | 5 |
| Edges | 0 | 12 | 8 |
| Faces | 1 | 6 | 5 |
