Although David is absolutely correct in his answer, I want to offer a different perspective.

For my assignment for procedural content generation, I looked at (among other things) icosahedron versus more traditional subdivided spheres. Look at these procedurally generated spheres:

Both look like perfectly valid spheres, right? Well, let's look at their wireframes:

Wow, what happened there? The wireframe version of the second sphere is so dense that it looks textured! I'll let you in on a secret: the second version is an icosahedron. It's an almost perfect sphere, but it comes at a high price.

Sphere 1 uses 31 subdivisions on the x-axis and 31 subdivisions on the z-axis, for a total of 620 faces.

Sphere 2 uses 5 recursive subdivisions, for a total of 109,220 faces.

But okay, that's not really fair. Let's scale down the quality considerably:

Sphere 1 uses 5 subdivisions on the x-axis and 5 subdivisions on the z-axis, for a total of 100 faces.

Sphere 2 uses 0 recursive subdivisions, for a total of 100 faces.

They use the same amount of faces, but in my opinion, the sphere on the left looks better. It looks less lumpy and a lot more round. Note also that the left sphere scales linearly (100 faces, 120 faces, etc.) while the right sphere scales exponentially (100, 420, 1700, 6820, 27300, 109220).

The truth is: you don't need the precision an icosahedron will give you. Because they both hide a much harder problem: texturing a 2D plane on a 3D sphere. Here's what the top looks like:

On the top-left, you can see the texture being used. Coincidentally, it's also being generated procedurally. (Hey, it was a course on procedural generation, right?)

It looks terrible, right? Well, this is as good as it's going to get. I got top marks for my texture mapping, because most people don't even get it this right.

So please, consider using cosine and sine to generate a sphere. It generates a lot less faces for the same amount of detail.

Although David is absolutely correct in his answer, I want to offer a different perspective.

For my assignment for procedural content generation, I looked at (among other things) icosahedron versus more traditional subdivided spheres. Look at these procedurally generated spheres:

Both look like perfectly valid spheres, right? Well, let's look at their wireframes:

Wow, what happened there? The wireframe version of the second sphere is so dense that it looks textured! I'll let you in on a secret: the second version is an icosahedron. It's an almost perfect sphere, but it comes at a high price.

Sphere 1 uses 31 subdivisions on the x-axis and 31 subdivisions on the z-axis, for a total of 3,844 faces.

Sphere 2 uses 5 recursive subdivisions, for a total of 109,220 faces.

But okay, that's not really fair. Let's scale down the quality considerably:

Sphere 1 uses 5 subdivisions on the x-axis and 5 subdivisions on the z-axis, for a total of 100 faces.

Sphere 2 uses 0 recursive subdivisions, for a total of 100 faces.

They use the same amount of faces, but in my opinion, the sphere on the left looks better. It looks less lumpy and a lot more round. Let's take a look at how many faces we generate with both methods.

Icosahedron:

• Level 0 - 100 faces
• Level 1 - 420 faces
• Level 2 - 1,700 faces
• Level 3 - 6,820 faces
• Level 4 - 27,300 faces
• Level 5 - 109,220 faces

Subdivided sphere:

• YZ: 5 - 100 faces
• YZ: 10 - 400 faces
• YZ: 15 - 900 faces
• YZ: 20 - 1,600 faces
• YZ: 25 - 2,500 faces
• YZ: 30 - 3,600 faces

As you can see, the icosahedron increases in faces at an exponential rate, to a third power! That is because for every triangle, we must subdivide them into three new triangles.

The truth is: you don't need the precision an icosahedron will give you. Because they both hide a much harder problem: texturing a 2D plane on a 3D sphere. Here's what the top looks like:

On the top-left, you can see the texture being used. Coincidentally, it's also being generated procedurally. (Hey, it was a course on procedural generation, right?)

It looks terrible, right? Well, this is as good as it's going to get. I got top marks for my texture mapping, because most people don't even get it this right.

So please, consider using cosine and sine to generate a sphere. It generates a lot less faces for the same amount of detail.