Let $G$ be a connected, planar graph for which every vertex has degree $3$ . Moreover, suppose there is a face of length at least $12$ .
Is it possible to construct an example of such $G $ whose only odd faces are six triangles, and for which no two such triangles share a common vertex?
(For my purposes I may assume there are no faces of length $1$ or $2$, in which case there must be an odd face of length at least 3. By the handshake lemma, there are an even number of, hence at least 2, such odd faces.)