Schläfli symbol calculator

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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:

P=2⋅n⋅b

However, there are many more "specific" formulas. It breaks problems into step-by-step solutions, showing how each part contributes to the answer.

In a hexagram, we can use the following formulas to calculate the various characteristic quantities:

​l=3⋅bb=3​a​c=b​

The factor 3​ comes from the intimate connection between hexagons and equilateral triangles: the angles of such a shape are, in fact, 60° (visit Omni's equilateral triangle calculator if you want to refresh your knowledge!).

This tool is built with learning in mind — for anyone who benefits from more explanation, structure, or time to connect the dots.

While most tools expect perfect input, Symbolab meets students in real life, scribbled pages, screenshots, and all, making help just a photo or screenshot away.

Here’s what sets this AI tool apart:

Step-by-Step Explanations: Many problems are broken down into clear, structured steps — helping students understand not just what to do, but why it works.

Covers a Wide Range of Subjects: From pre-algebra through calculus, from trigonometry to physics and statistics—Symbolab’s AI-powered tool is a useful companion at different learning stages.

Interactive Practice and Feedback: Offers a variety of practice problems, customizable quizzes, and real-time feedback designed to reinforce learning over time.

Built-in Learning Tools: Includes Notebooks, cheat sheets, group study options, and solution verification, quiet support for independent learners who just need a little structure.

Simple and Accessible: A clean design, an intuitive math keyboard, and support for both symbols and plain language help keep the focus on learning — not on figuring out how to use the tool.

Symbolab was built with one belief at its core: everyone deserves a way to understand math, not just survive it.

Star Shape Calculator

Twinkle, twinkle, little star...

The formula is:

​A=(4⋅2a​⋅d2−(2a​)2​)+(2⋅a2⋅cot(8π​))​

You can build star shapes for any regular polygon: the series continues with the enneagram, the decagram, etc. 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.

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. This AI-powered tool is designed to do more — by helping students understand the steps behind the solution, gives something more understanding.

    That’s the key difference.

    if was in e.g. It analyzes what kind of problem has been inputted such as an equation, an integral, a system of inequalities, and generates the best way forward.

    Whether a problem is typed, spoken in everyday language, or shared as a photo from a notebook, our AI is designed to help interpret and respond to it.

    This flexibility matters, because sometimes learners don’t remember every symbol.

    schläfli symbol calculator

    The flag of Jordan depicts a heptagram; the shape was also part of the old Georgian coat of arms. Of the 196 country flags in the world, 40 of them contain stars. In fact, you can consider the hexagram itself as the result of the intersection of two equilateral triangles with side times larger than the side of the hexagram.

    This interesting symmetry comes from the extreme regularity of hexagons.

    Learn more with the star shape calculator at Omni Calculator!

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Most calculators are built to compute and move on. And that’s okay

Symbolab’s AI Math Calculator is designed to meet students where they are and help them move forward.

Chooses a Structured Approach That Supports Understanding

Understanding the problem is just the beginning.

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. function walk(i) { if(Schlafli_P <= 2 * Schlafli_Q) return false; collection[i].forEach((e, i, a) => { turtle.jump(e); turtle.goto(a[(i+1)%a.length]); }); return i < collection.length - 1; } function getSchlafiCollection(Schlafli_P, Schlafli_Q, radius) { const points = Array.from({length: Schlafli_P}).map((e, i, a, f=i*2*Math.PI/a.length) => [radius * Math.sin(f),radius * -Math.cos(f)]); const cycle = []; for(let i = 0; !cycle.includes((i * Schlafli_Q) % Schlafli_P); i++) { cycle.push((i * Schlafli_Q) % Schlafli_P); } const collection = []; for(let i = 0; i < points.length / cycle.length; i++) { const rot = rot2(i * 2 * Math.PI / Schlafli_P); collection.push(cycle.map((e, i) => trans2(rot, points[cycle[i] % points.length]))); } return collection; } function rot2(a) { return [Math.cos(a), -Math.sin(a), Math.sin(a), Math.cos(a)]; } function trans2(m, a) { return [m[0]*a[0]+m[2]*a[1], m[1]*a[0]+m[3]*a[1]]; } //Matrix(2x1) x Matrix(2x2) //////////////////////////////////////////////////////////////// // Text utility code.

The pentagram is nothing but a five-pointed star shape. It supports topics such as algebra, calculus, trigonometry, and more.

If a problem looks confusing, Symbolab’s AI Math Solver is built to slow down the explanation.

const Schlafli_P = 5; //min=3 max=60 step=1 const Schlafli_Q = 2; //min=1 max=30 step=1 const radius = 54; //min=1 max=100 step=1 // You can find the Turtle API reference here: https://turtletoy.net/syntax Canvas.setpenopacity(1); // Global code will be evaluated once.

For the perimeter, use the general formula above, substituting n=5. Learn everything about this "magic" number at the golden ratio calculator!

Apart from those golden ratios, there are a couple more relationships holding in a five-pointed star shape:

​a=b+cl=a+b​

We can also calculate the value of the perimeter and the area.

degrees mode (or any other) //////////////////////////////////////////////////////////////// function Text() {class Text {print (t, str, scale = 1, italic = 0, kerning = 1) {let fc = t._fullCircle;t.radians();let pos = [t.x(), t.y()], h = t.h(), o = pos;str.split('').map(c => {const i = c.charCodeAt(0) - 32;if (i < 0 ) {pos = o = this.rotAdd([0, 48*scale], o, h);} else if (i > 96 ) {pos = this.rotAdd([16*scale, 0], o, h);} else {const d = dat[i], lt = d[0]*scale, rt = d[1]*scale, paths = d[2];paths.map( p => {t.up();p.map( s=> {t.goto(this.rotAdd([(s[0]-s[1]*italic)*scale - lt, s[1]*scale], pos, h));t.down();});});pos = this.rotAdd([(rt - lt)*kerning, 0], pos, h);}});t._fullCircle = fc;}rotAdd (a, b, h) {return [Math.cos(h)*a[0] - Math.sin(h)*a[1] + b[0], Math.cos(h)*a[1] + Math.split('>').map(r=> { return [r.charCodeAt(0)-106,r.charCodeAt(1)-106, r.substr(2).split('<').map(a => {const ret = []; for (let i=0; i<a.length; i+=2) {ret.push(a.substr(i, 2).split('').map(b => b.charCodeAt(0)-106));} return ret; })]; });return new Text();}

AI Math Calculator

All About Symbolab’s Online AI Math Solver & Calculator

Getting the right answer in math is important, but what really matters is knowing how you got there, and being able to do it again the next time.

We start drawing it from an octagon, an eight-sided polygon.

As for the heptagon, we deal with a shape with three boundaries (we can identify both 8/2 and 8/3). If an equation needs factoring, it shows how.