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I think that they have Seifert fiber space presentation as: $(On,1|(1,b))$.

Or $(On,1|(1,b),(a_1,b_1),...,(a_r,b_r))$, if you allow an orbifold with cone points in $RP^2$.

You can look at the cases by decomposing $RP^2=Mo\cup_{\partial}D$, so the orientable 3-manifold will be the

1) orientable $Q=Mo\times^~S^1$, Q=Mo\tilde{\times}S^1$, the twisted circle bundle over the mobius band, very well known being equivalent to the orientable I-bundle over the Klein bottle, with boundary a torus$T$, 2) and a Dehn-filling in the remaining disk$D$, with a whichever fibered solid torus or tori. We could say that$(On,1\mid (1,b))=Q\cup_T W(1,b)$, for a fibered$(1,b)$solid torus$W$4 some enhancements; added 36 characters in body I think that they have Seifert fiber space presentation as:$(On,1|(1,b))$. Or$(On,1|(1,b),(a_1,b_1),...,(a_r,b_r))$, if you allow an orbifold with cone points in$RP^2$. You can look at the cases by decomposing$RP^2=Mo\cup_{\partial}D$,so RP^2=Mo\cup_{\partial}D$, so the orientable 3-manifold will be the

1) orientable $Mo\times^~S^1$ "Q=Mo\times^~S^1$, the twisted circle bundle over the mobius band(, very well known as being equivalent to the orientable I-bundle over the Klein bottle), with boundary a torus$T$, 2) and a Dehn-filling in the remaining disk$D$, with a whichever fibered solid torus or tori..tori. We could say that$(On,1\mid (1,b))=Q\cup_T W(1,b)$, for a fibered$(1,b)$solid torus$W$3 added 1 characters in body I think that they have Seifert fiber space presentation as:$(On,1|(1,b)$.(On,1|(1,b))$.

Or $(On,1|(1,b),(a_1,b_1),...,(a_r,b_r))$, if you allow an orbifold with cone points in $RP^2$.

You can look at the cases by decomposing $RP^2=Mo\cup_{\partial}D$,so the orientable 3-manifold will be the

1) orientable $Mo\times^~S^1$ "twisted circle bundle over the mobius band (well known as the orientable I-bundle over the Klein bottle)

2) and a Dehn-filling in the remaining disk $D$, with a whichever fibered solid torus or tori...

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