Schläfli symbol calculator
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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. Admire the proportions of these quantities:
al=ba=cb=φ
Knowing this, we can almost understand why the pentagram got its reputation!
It shows what to do first, how each step builds on the last, and how each move brings you closer to the solution. 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. 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.
Well, everything apart from occultism: we deal with geometry, not magic! What matters next is how to work through it in a way that builds clarity and confidence.
Symbolab’s AI Math Calculator doesn’t just display a final answer. 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°.
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.
In the case of a pentagram, the same couple would be a pair separated by a single side (thus a "first-order" ray), while in a hexagram, the same couple is parallel.
When drawing a heptagram then, we meet two star-shaped polygons: a stubbier one, associated with the Schläfli symbol 7/2, and a more slender one with symbol 7/3.
We call the side of the 7/3 heptagram d.
Here are the formulas for the side: don't worry if you see some 2 factors, blame trigonometry instead!
a=2⋅b⋅sin(135)c=b⋅2d=b+c
As for the heptagram, the fastest way to compute the area involves the separation of the octagram in an octagon with side a and eight triangles. How many triangles are in a pentagram shape?
We counted...
Learn more with the star shape calculator at Omni Calculator!
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It’s designed to support learning. Not with flashy features or shortcuts—but by offering clear, step-by-step explanations designed to support learning.Solutions are broken down in a structured way, helping users follow the logic behind each step — why it comes next and how it builds on the one before.
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! Of the 196 country flags in the world, 40 of them contain stars.
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.
Some facts about star shapes!
Star polygons are simple shapes, but somehow they keep appearing all around us.
Consider flags, for example.
But you knew this already: everyone draws stars in their lives!
The pentagram got a bad reputation due to its association with evil: don't trust such voices and keep exploring this fascinating shape's geometry!
Here is a pentagram with all the important features highlighted!
You will meet these elements in all the other star polygons in this calculator: pay attention!
You can identify:
- a, the distance between two contiguous "points" of the star;
- b, the length of the first set of "rays" wounding around the polygon;
- c, the side of the original polygon; and
- l, the distance from two "points" of the stars belonging to the same side of the polygon.
Note that connecting the points of the star creates a new n-sided regular polygon with side a!
Some relationships between those quantities always hold (for every star polygon); others are specific for a given shape.
if was in e.g.