Schläfli symbol calculator

Find out more about hexagon symmetries with our hexagon calculator.

We can calculate the area of a hexagram with the formula:

Increase the number of sides and get a heptagram, a seven-pointed star. For anyone who’s ever stared at a math problem and thought, I just need someone to show me, Symbolab’s AI Math Solver offers a structured, supportive way to work through the steps.

Why a Math Solver Matters More Than a Calculator

When the numbers stop adding up, the instinct is often to grab a calculator.

By definition, they are:

• Non-convex;
• Self-intersecting;
• Equilateral; and
• Equiangular polygons.

Let's look at all of these features one by one!

• Non-convex means that you can draw a line between two points inside the star-shaped polygon that passes outside its perimeter.
• Self-intersecting means that you can build all the different star shapes starting from a regular polygon and prolonging its vertexes until the extensions cross each other.
• Equilateral signifies that all the outer sides of the star-shaped polygon have the same length (latus is the Latin for side).
• Equiangular means that all the angles lying in the same "region" are equal.

The last two attributes of the star polygons automatically qualify them as regular polygons.

Sometimes they only know how to describe what they’re trying to do. The formula for the perimeter of a pentagram shape is:

where is the length of the side of the "rays" of our star. const turtle = new Turtle(); const text = new Text(); const collection = getSchlafiCollection(Schlafli_P, Schlafli_Q, radius); let width = 0; for(let i = -1; i < 1; i++) { turtle.jump(0 - width, 93 + i * 300); if(Schlafli_P <= 2 * Schlafli_Q) { text.print(turtle, 'Schlafli_P should be larger than 2 * Schlafli_Q', .2); } else if(Schlafli_Q == 1) { text.print(turtle, '- Convex polygon {' + Schlafli_P + '} -', .2); } else { text.print(turtle, '- Star polygon {' + Schlafli_P + '/' + Schlafli_Q + '} -', .2); } width = turtle.pos()[0] / 2; } // The walk function will be called until it returns false.

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.

In particular, you can draw it from a pentagon.

🔎 You can draw a pentagram without separating the pen from the paper. It’s not about rushing to the right answer. Over time, this makes math feel less like guessing—and more like following a path you understand. 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.

The pentagram is nothing but a five-pointed star shape. Of the 196 country flags in the world, 40 of them contain stars. For example, you can insert the area, and we will tell you all the other lengths.

⚠️ The cotangent function in the area formulas of heptagrams and octagrams prevents the calculations from running in the inverse direction!