Shapes are weird, but we all probably have memories identifying squares and circles from drawings or like little blocks. Specifically the brightly colored ones you would like slide around on your desk or whatever. Most of those shapes were like… normal though. Maybe the weirdest one was a hexagon or something. But what are some *weird* shapes? What’s the *weirdest* shape?

**Dodecahedrons and Regular Polygons**

Honestly the dodecahedron isn’t really an interesting shape. It’s just a polygon with 12 sides, we’re bringing it up because knowing what a 12-sided shape was called was like the ultimate trivia fact to have on hand in elementary school.

This does give us a chance to talk about regular polygons. A regular polygon is a shape where all sides and angles are equal. So all the sides are the same length and all the angles are equal in measure. Take a square. All four sides are the same, and all angles are 90 degrees. That’s a regular polygon for you.

You’re probably most familiar with regular polygons in their convex form. That’s the flat way you probably imagine a shape. Regular polygons can also be skew or star. The former just means not all the shape’s points are on the same plane (it’s in 3-D). Skew polygons need at least four points. A cube is a type of skew polygon, but it’s a type of octagon instead of a rectangle. Because cubes have eight vertices. So there’s a fun trivia fact for you.

Star polygons can be made by overlaying shapes on top of each other. You can make a regular star polygon by taking an equilateral triangle and laying another one on top of it upside down. That makes a hexagram–but you might know it as a Star of David.

**Rhombicosidodecahedron**

Once you get into *weird shapes* you start to remember why you can study geometry for a living. Because some of these shapes will make you ask “why?”

Enter the rhombicosidodecahedron. Every single one of its faces are made of regular polygons. 20 of them are triangles, 30 are squares, and 12 are pentagons. This monster of a shape was named by Johannes Kepler as a shortened form of “truncated icosidodecahedron rhombus”.

The *next level* rhombicosidodecahedron is a truncated rhombicosidodecahedron, whose faces are 12 decagons (10 sided polygon), 30 octagons, 20 hexagons, and 60 squares.

**The Squircle**

You know how every part of corporate graphic design is going for simple and single-colored designs (probably also pastel colored?) where all edges and corners are rounded to make you *think* of a square but not really *be* a square. Then all details are simplified into oblivion until everything is just like… a letter with a color.

Anyway the shape of your iPhone’s app icons has a name. It’s called a squircle. It’s not a weird shape but it’s a funny name.

**Napkin Rings**

Are napkin rings weird on their own? No, but they do have a problem named after them.

So if you core a sphere, ergo you cut a cylinder out of the middle, you get what looks like a napkin ring. No matter the radius of the sphere, the resulting napkin ring will *always* have the same volume, because the volume of a napkin ring is dependent only on its height and not its radius.

That means if you made a napkin ring out of the Sun it would have the same volume as a napkin ring made out of a billiard ball.

**The Gömböc**

The Gömböc is the first time a mono-monostatic body has been realized in physical space. Being mono-monostatic means that when it’s on a flat surface it has exactly one stable and one unstable point of equilibrium (meaning the net forces on the object are zero). Another example of a mono-monostatic body is one of those tilting toys that gets up every time you try and tip it over.

Anyway, the fun part of the Gömböc is its relation to tortoises. The shapes of their shells are mono-monostatic bodies, allowing them to roll over a lot easier when they get flipped upside down onto their shells.

*See if you can name these much more normal looking shapes here.*