- Let p,q be two relatively prime positive integers.In euclidean 3-space,let P be a regular polygon region in the plane with centre of gravity origin and vertices $a_0,a_1,...,a_{p-1}$,and let X be the solid double pyramid formed from P by joining each of its points by straight lines to the points $b_0=(0,0,1)$ and $b_q=(0,0,-1)$ of $\mathbb E^3$.Identify the triangles with vertices $a_i,a_{i+1},b_0$,and $a_{i+q},a_{i+q+1},b_q$ for each $I=0,1,...,p-1$,in such a way that $a_i$ is identified to $a_{i+q}$,$a_{i+1}$ to $a_{i+q+1}$,and $b_o$ to $b_q$(subscripts are read mod p).Prove that the resulting space is homeomorphic to the Lens space $L(p,q)$.
It's difficult for me to imagine it intuitively,some advice?