A standard five-pointed star has 5 vertices. Each outer tip of the star counts as one vertex, so the number of vertices always matches the number of points. A six-pointed star has 6 vertices, a seven-pointed star has 7, and so on.
How Vertices Work in Star Shapes
In geometry, a vertex is any corner where two lines meet. On a star, the sharp outer tips are the vertices. A five-pointed star (called a pentagram) is a regular polygon with exactly five vertices and five edges connecting them. The key relationship is simple: an n-pointed star always has n vertices.
This holds true regardless of how the star is drawn. Mathematicians describe star shapes using the notation star(n, s), where n is the number of points placed equally around a circle and s determines which points get connected. In star(5, 2), for example, you place 5 points on a circle and draw lines connecting every 2nd point, producing the classic five-pointed star with 5 vertices. Changing the s value changes how the star looks (making it more or less “spiky”) but never changes the vertex count.
Vertex Counts for Common Stars
- Five-pointed star (pentagram): 5 vertices
- Six-pointed star (hexagram/Star of David): 6 vertices
- Seven-pointed star (heptagram): 7 vertices
- Eight-pointed star (octagram): 8 vertices
If you’re counting for a homework problem or a geometry exercise, just count the outer points. Each point is one vertex. The inner corners where lines cross inside the star are intersections, not vertices of the star polygon itself.
Why Some People Count 10 Vertices
Here’s where it gets confusing. Some teachers and worksheets ask students to count all the corners in a star shape, including the inner “dents” between the points. A five-pointed star drawn as a solid outline has 5 outer tips and 5 inner notches, giving 10 corners total. This applies when the star is treated as a concave polygon (a single closed shape with indentations) rather than as a star polygon made from intersecting lines.
Which answer is correct depends on context. If the star is drawn as a simple outline with alternating pointy and notched corners, the answer is 10 for a five-pointed star. If the star is defined as a star polygon in the mathematical sense, connecting every second point on a circle, the answer is 5. When in doubt, count every corner where the outline changes direction.
Stars in Nature Are Actually Spheres
If your question was partly inspired by curiosity about actual stars in the sky, those have zero vertices. Real stars are massive balls of hot gas, and their shape is nearly perfectly spherical. Astronomers measuring the precise shape of distant stars have found them to be round or very slightly elongated, with polar and equatorial radii differing by roughly 2% at most. The pointy shape we draw is an optical effect caused by the way light diffracts in our eyes and through telescope optics.
Starfish, despite the name, also don’t have true geometric vertices. Most species have 5 arms radiating from a central disc, though some have 6 or 7, and certain Antarctic species can grow more than 50 arms. Their tips are rounded, not angular, so “points” is more accurate than “vertices” in their case.