# Thread: Cyclic polytopes | polytopes with MANY faces

1. ## Cyclic polytopes | polytopes with MANY faces

I want to find sample input of BIG data for a program.

I am interested in polytopes with many faces. I want the half-spaces that define the polytope to be as many as possible.

I do not care if it is a random polytope or a real one (I mean one with a name, like a cube for example (which is defined by only 6 faces)).

I want the polytope(s) to be defined by vertices or by half-spaces.

2. Catalan solid ones seem to be ideal, since they can have many faces. Moreover they are all convex which is good for me.
However, I am having troubles locating their vertices!!

EDIT: It seems that I am going to do that by hand ;p

3. Ok as I said above, I am getting the data by hand. I have stuck here:
Code:
```For a snub cube with unit edge length, use all the even permutations of
( C_1,C_2,C_3)
having an even number of plus signs, along with all the odd permutations having an odd number of plus signs.```
I am not sure which is the result of these operations. Can anybody help?

4. I don't think it's possible to write a single structure to represent all polytopes (because of how the half-spaces are calculated) but it is possible to write polymorphic code!

For example, to make a tetrahedron :
Code:
```struct vertex {

double x, y, z;
};

struct tetra {

array<struct vertex, 4> p;

array<double, 4> a, b, c, d;
};```
Here each index of a, b, c and represent the plane of each face taken from the equation ax + by + cz - d = constant and p is storage of 4 vertices of the tetrahedron.

You can easily create a base polymorphic polytope class which stores all the functions you'll need (calculating half-spaces and if you want, point location routines) and from there, you can use derived classes to implement each specific polytope you want to model.

It's because some polytopes have faces made out of more than 3 points or some get really funky so you need specific classes for each case, I think.