Schläfli symbol calculator
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If an equation needs factoring, it shows how. To build it starting from a regular n-polygon like a pentagon (), hexagon (), etc., follow these steps:
- Prolong the sides of the starting polygon.
- Extend each side until it intersects the prolongation of the next non-adjacent side.
For odd-sided polygons, you can have an intersection between prolongations separated by an increasing number of sides: check all the possibilities!
Are there star-shaped polygons you can't draw without lifting the pen from the paper?
No! If you are dealing with regular star-shaped polygons, you can always find a way to draw the entire shape without lifting the pen from the paper.
Well, everything apart from occultism: we deal with geometry, not magic! 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. However, humanity covered it with a fair dose of mysticism.
The flag of Jordan depicts a heptagram; the shape was also part of the old Georgian coat of arms.
It’s quick. We can calculate the geometric relationships for both shapes, but we warn you: we will use some trigonometry, and the formulas will start to look "ugly"!
a=2⋅b⋅sin(2180−(360/7))c=2⋅b⋅cos(7360)
The side of the boundary 7/3 comes from the formula:
d=2×cos(180−2×7360)l−l
The formula for the area requires we compute:
- The area of a heptagram with a side equal to a; and
- Seven times the area of an isosceles triangle with side d and base a.
A=(27⋅2a⋅d2−(2a)2)+(47⋅a2⋅cot(7π))
To conclude, the last "manageable" star-shaped polygon is the octagram, an eight-pointed star shape with an intriguing figure, rich in angles of 45°.
To the stars, with Omni Star Shape Calculator!
Star shapes: pointy geometry
Star polygons are the shiniest shapes in geometry. For the perimeter, use the general formula above, substituting n=5. The designers of the national colors couldn't make up their minds!
Our favorite starred flag is the flag of Nepal: the only non-rectangular flag in the world also has a beautiful 12-pointed star which really makes it stand out!
Star-shaped polygons appear widely through sacred geometry.
It highlights the rules in play and helps students see patterns. If a limit needs the chain rule, it explains why. 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.
Symbolab uses AI to analyze each problem to generate step-by-step, solutions aimed at supporting learning— not just computation. if was in e.g. In particular, you can draw it from a pentagon.
🔎 You can draw a pentagram without separating the pen from the paper. That’s a quiet but powerful difference.
The AI is designed to respond in a clear, helpful, and reassuring way, encouraging you to take another look with confidence.
Practice Problems: Explore a wide range of examples, supported by hints designed to guide you towards the next step.
Quizzes: See how far you've come, with feedback that feels more like a mirror than a grade.
Because real understanding isn’t fast.
Rather than relying on rigid, pre-programmed steps. 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. 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...
It shows what to do first, how each step builds on the last, and how each move brings you closer to the solution. Only Azerbaijan contains an octagram!
Many countries have pentagrams in their flags: there is quite a constellation from the US to Somalia!
An old flag of Australia contained six-pointed stars, while the modern one has both a pentagram and some heptagrams!
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.