edges is preserved, the outer edge distance is also preserved. The epsilon coefficients depend only on the outer edge distance and the distinction between inner and outer edges, so it follows that the epsilon coefficients of $M_{2N+1}$ and $\alpha(M_{2N+1})$ are the same.

Finally, we can see from Figure \[FigureM\_2N+1\] that $\alpha$ either preserves all or reverses all the orientations on edges.

To prove that $M_{2N+1}$ is intrinsically chiral, we will use the following Proposition whose proof is similar to that of Theorem \[k7 chiral\].

\[intrinsic chirality\] Let $G$ be an oriented graph with a generalized Simon invariant $\widehat{L}_{\varepsilon}(f)$. Suppose that $\widehat{L}_{\varepsilon}(f)$ is odd for every embedding $f: G \rightarrow {S}^3$, and every automorphism of $G$ preserves the epsilon coefficients of $G$ and either preserves the orientation of every edge or reverses the orientation of every edge. Then $G$ is intrinsically chiral.

For the sake of contradiction, suppose that for some embedding $f$ of $G$, there is an orientation reversing homeomorphism $h$ of the pair (${S}^3$, $f(G)$). Let $\alpha$ denote the automorphism that $h$ induces on $G$.

Fix a sphere of projection $P$ in $S^3$. Since $f\circ \alpha(G)$ and $f(G)$ are identical as subsets of $S^3$, their projections on $P$ are 