Is it possible for a bicyclo compound to have three bridges of equal length? My teacher told me that the value of $x$ is always greater than or equal to $y$ and that y is always greater than $z$ in a bicyclo compound, where $(x,y,z)$ are the lengths of the bridges.



But in this compound $x = y = z$.
Can someone clarify?
Why not? The simplest bicyclic bridged compound, bicyclo[1.1.1]pentane, is a well-known example of such a molecule for its use in synthesizing the even more strained propellane. I believe your teacher was trying to prescribe the rules of bicyclic nomenclature, i.e.


  In between the prefix and the suffix, a pair of brackets with numerals denotes the number of carbon atoms between each of the bridgehead atoms. These numbers are arranged in descending order and are separated by periods.