Schläfli symbol calculator

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!

It highlights the rules in play and helps students see patterns. The formula for the perimeter of a pentagram shape is:

where is the length of the side of the "rays" of our star. But it doesn’t teach. If an equation needs factoring, it shows how. When we use this value in a trigonometric function like the tangent, we find tan60°=3​. The hexagram "rays" are nothing but equilateral triangles.

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! 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.

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. Sometimes they only know how to describe what they’re trying to do.

Most calculators are built to compute and move on. It looks like someone really put a lot of thought into such a simple geometric shape. How many triangles are in a pentagram shape?

We counted... It breaks problems into step-by-step solutions, showing how each part contributes to the answer. 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.

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 . It shows what to do first, how each step builds on the last, and how each move brings you closer to the solution.

It’s familiar. if was in e.g. 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. For the area, a specific formula is needed: