I have a problem on N-Dimensional polytopes and their construction using lesser-dimensional polytopes. i have read at this wikipedia article that a N-dimensional polytopes has $V$ vertices, $L$ lines, $F$ faces, $C_1$ cubes, $C_2$ tesseracts, and so on. this allows a formula of the form: (also, the exponents are not exponents, just another subscript type)
$$ \begin{align} V^1*2&=V^2\\ V^X*2&=V^{X+1}\\ (L^2)\times 2+ V^1&=L^3\\ (L^X)\times 2+ V^{X-1}&=L^{X+1}\\ (F^3)\times 2+ L^2&=F^4\\ (F^X)\times 2+ L^{X-1}&=F^{X+1}\\ ({C_1}^4)\times 2+ F^3&={C_1}^5\\ ({C_1}^X)\times 2+ F^{X-1}&={C_1}^{X+1}\\ ({C_Y}^X)\times 2+ C_{Y-1}^{X-1}&=C_{Y+1}^{X+1}\\ \end{align} $$
This is the Method I found out from the wikipedia article. Basically, if you take the $C_{Y}^{X}$ and create another one of $C_{Y}^{X}$, parallel to the first one, and then link the two with $L^{X-1}$ lines, thus creating all the $C_Y$ and less criteria for the link's specifications.
The problem is, i looked on Wikipedia, and there is nothing on the other types of polytopes. can someone show the formula like mine that works for anything involving, starting with the dodecahedron? Thanks in advance.