It’s an octagon. Honestly, you probably knew that already. But there is a massive difference between knowing the name of a shape and actually understanding how it functions in the real world, from the architectural blueprints of ancient cathedrals to the terrifyingly efficient design of a stop sign.
Shapes govern our lives. We don't think about it much, but the geometry surrounding us dictates how we move through space. When you ask what is an 8 sided shape called, you're usually looking for a quick answer for a crossword or a homework assignment, but the rabbit hole goes way deeper than a simple Greek prefix.
The word itself comes from the Greek oktágōnon, which literally translates to "eight angles." It makes sense. If you have eight sides, you’ve gotta have eight angles. But here is where it gets weird: not every octagon looks like the one you see at a four-way intersection.
The Regular Octagon: Geometry’s Gold Standard
Most people picture a "regular" octagon. This is the symmetrical beauty where every side is the exact same length and every internal angle is precisely 135 degrees. If you add those up, you get a total interior sum of 1080 degrees.
Why 135? Math. Specifically, the formula $(n-2) \times 180 / n$. If you plug in 8 for $n$, you get the magic number.
But what about the "irregular" ones? They’re still octagons. An 8 sided shape can look like a jagged star, a stretched-out rectangle with the corners clipped, or even something that resembles a weirdly shaped L. As long as it has eight straight sides that close into a single loop, it qualifies. You could draw a shape that looks like a squashed spider, and if it has eight distinct line segments, it’s legally an octagon in the eyes of geometry.
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Concave vs. Convex: The "Cave" Rule
You’ve probably seen shapes that look like they’ve been dented. Those are concave octagons.
Think of it this way: if any part of the shape "points" inward, it’s concave. In technical terms, if you can draw a line between two points inside the shape and that line passes outside the shape, it’s concave. Convex octagons, like the stop sign, have all their vertices pointing outward. Most people prefer the convex ones. They're tidier.
Why the Stop Sign Is the Way It Is
Ever wonder why we chose an 8 sided shape for stop signs? It wasn't random.
Back in the early 1920s, the Mississippi Valley Association of State Highway Departments met to standardize road signs. They had a clever idea: use the number of sides to indicate the level of danger. A circle (infinite sides) meant the highest danger—railroad crossings. The octagon was chosen for the second-highest level of danger. It was unique.
It stands out. Drivers can recognize an octagon from the back, even if the sign is covered in snow or mud. That distinct silhouette tells you to tap the brakes before you can even read the word "STOP." It’s a masterclass in UX design from a time before UX design was even a buzzword.
Octagons in Architecture: More Than Just Pretty
If you look at the Dome of the Rock in Jerusalem or the Castel del Monte in Italy, you’ll see the octagon everywhere. Why? Because it’s the perfect bridge.
Architects use the octagon to transition between a square base and a circular dome. It’s hard to put a round lid on a square box. But if you shave the corners off that square, you get an octagon. It provides more support points for a dome than a square does, making the whole structure sturdier without the complexity of building a perfect circle from the ground up.
In many cultures, this shape represents the "middle ground" between the earth (often symbolized by a square) and the heavens (symbolized by a circle). It’s the transitional space. It’s why you see so many octagonal baptismal fonts in old churches—it’s the step between one world and the next.
Nature's 8 Sided Secrets
Nature doesn't usually do straight lines. You won't find many perfect octagons in the wild.
But look at a honeycomb. Bees use hexagons because they tile perfectly without leaving gaps. An octagon doesn't do that. If you try to floor a room with only regular octagons, you’ll end up with little square gaps between them. Tiling experts call this "truncated square tiling." It looks great in a Victorian bathroom, but for a bee trying to maximize honey storage, it’s a waste of space.
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However, the number eight is everywhere. Spiders. Octopuses. The symmetry of a starfish. While these aren't geometric polygons, the "eight-ness" of their biology serves a purpose. It provides a balance of mobility and stability that four or six limbs just can’t match in certain environments.
The Math You Can Actually Use
If you’re building a DIY project—maybe an octagonal planter or a poker table—you need to know the cut angle. This is where most people mess up.
To make a perfect 8 sided shape, you don't cut your wood at 45 degrees. You cut it at 22.5 degrees.
Why? Because you have eight joints. Each joint consists of two pieces of wood meeting. To get that 135-degree internal angle, each piece needs to contribute half of the remaining angle. It’s a classic woodworking blunder to cut at 45 and realize you’ve built a square instead of an octagon.
Calculating Area (The Hard Way vs. The Easy Way)
If you have a regular octagon and you need to find the area, you could use a complex formula involving the apothem (the distance from the center to the midpoint of a side).
The formal math looks like this:
$$Area = 2(1 + \sqrt{2})s^2$$
Where $s$ is the length of one side.
But if you aren't a math nerd, there’s a "cheat" method. Imagine the octagon is just a large square with the four corners cut off. Calculate the area of the big square, then subtract the area of the four triangles you "cut" from the corners. It’s much more intuitive for most people.
Cultural Weirdness and 8 Sided Luck
In Chinese culture, the octagon is often associated with the Bagua—eight symbols used in Taoist cosmology to represent the fundamental principles of reality. You'll see octagonal mirrors (Bagua mirrors) hung over doors to ward off negative energy.
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It’s also common in martial arts. The UFC "Octagon" isn't just a cool-sounding name. The 8 sided fence was specifically designed to prevent any fighter from getting stuck in a corner, which happens in a square boxing ring. The wider angles of the octagon make it easier to escape a clinch. It changed the entire strategy of the sport.
Summary of 8 Sided Facts
- Official Name: Octagon.
- Internal Angles: 135 degrees (for a regular one).
- Sum of Angles: 1080 degrees.
- Types: Convex (points out), Concave (points in), Regular (equal sides), Irregular (different sides).
- Common Uses: Stop signs, UFC cages, architectural domes, umbrellas.
Understanding what is an 8 sided shape called is just the tip of the iceberg. Whether you're recognizing it on the road or calculating the area for a home renovation, the octagon is one of the most functional and visually striking polygons in our geometric toolkit.
To apply this knowledge practically, start by observing your surroundings. Count the sides of the nuts in a hardware store or the pattern on a tiled floor. If you're planning a construction project involving an octagon, always remember the 22.5-degree miter cut rule to ensure your angles line up perfectly. For those interested in design, consider using octagonal layouts to create better flow in small spaces where 90-degree corners feel too restrictive.