Schläfli symbol calculator

Our star shape calculator can help you calculate all of the characteristic lengths of the four most common star-shaped polygons:

• Pentagram;
• Hexagram;
• Heptagram; and
• Octagram.

Select the desired number of sides at the top of the calculator and insert the value of one of the available variables there: we will calculate all the others!

The AI is designed to respond in a clear, helpful, and reassuring way, encouraging you to take another look with confidence.

Because real understanding isn’t fast.

Do we need to mention the Star of David, a hexagram, or the shared symbolism associated with the pentagram from Hinduism to Neo-paganism?

You can also notice that the constructions of a star-shaped polygon create many triangles, the simplest bi-dimensional shape.

To make the game more entertaining, connect the outside points of the n-gram!

Rather than relying on rigid, pre-programmed steps. Keep reading to find out:

• What are star-shaped polygons;
• How to build them;
• What is the pentagram: a down to Earth introduction;
• Other star-shaped polygons; and
• How to use our star shape calculator.

We also added some fun facts about these shapes and a challenge: how many triangles are in a pentagram?

The heptagram has a particularity: it is the first star-shaped polygon for which we can naturally find a third boundary.

The reason for this peculiarity is that two sides of a heptagon separated by two others can finally meet if prolonged. A generalization of the formulas is hardly helpful since every new odd-numbered polygon is associated with an additional boundary: for the enneagram, we can identify the Schläfli symbol 9/4, for the hendecagram, we have the boundary 11/5, and so on.

Star polygons are simple shapes, but somehow they keep appearing all around us.

Consider flags, for example.

The formula for the perimeter of a pentagram shape is:

where is the length of the side of the "rays" of our star. It looks like someone really put a lot of thought into such a simple geometric shape. However, humanity covered it with a fair dose of mysticism. It is the first regular star polygon we can build by extending the sides of a polygon (try to do that with a square or a triangle, and you will understand), and also one of the most drawn shapes in the world.

The formula is:

You can build star shapes for any regular polygon: the series continues with the enneagram, the decagram, etc. It’s designed to break things down clearly, to make complex parts feel more manageable— without rushing or skipping essential steps.

And when the path still feels tangled, there’s help without judgment:

1. Chat with Symbo: You can ask about any step — big or small.

   Its features were built with the student experience in mind: the stress of not knowing where to start, the frustration of getting stuck halfway, the quiet relief when something finally makes sense.

   From the way it breaks down complex steps to how it gently explains why each one matters, Symbolab’s AI Math Calculator helps make math problems feel more approachable and manageable.

   Since there are five rays, with two sides each, to calculate the perimeter of the pentagram, it suffices to count ten times the length of .

The answer is . Admire the proportions of these quantities:

Knowing this, we can almost understand why the pentagram got its reputation!

Let's check the general ones first:

• The "side" of a star is given by the sum l=c+2⋅b; and
• You can calculate the perimeter of the first boundary of an n-pointed star with the formula:

However, there are many more "specific" formulas. It provides step-by-step explanations tailored to the type of problem at hand.

If a limit needs the chain rule, it explains why. if was in e.g. It’s about building understanding, one step at a time.

Step-by-Step Solutions

This is where Symbolab’s AI Math Calculator stands out. It’s quick.