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My question was partly inspired by the question linked below.

• There is a 3-connected 5-regular simple $n$-vertex planar graph iff $n$ satisfies....?

I see a wonderful construction of Adam P. Goucher, which guarantees that 3-connected 5-regular planar graphs are infinitely numerous. I wonder if there is also such a construct for the 5-connected 5-regular planar graphs. (Maybe I don't need to generate all of them like the title of this post.)

I noted the number of 5-connected 5-regular planar graphs with at most 36 vertices in the following paper.

• Hasheminezhad M, McKay B, Reeves T. Recursive generation of simple planar 5-regular graphs and pentangulations[J]. 2011.

Enough such graphs to convince me there are an unlimited number of such graphs. And when $n$ is large enough, for every $n$ there is a graph that I want.

My question was partly inspired by the question linked below.

• There is a 3-connected 5-regular simple $n$-vertex planar graph iff $n$ satisfies....?

I see a wonderful construction of Adam P. Goucher, which guarantees that 3-connected 5-regular planar graphs are infinitely numerous. I wonder if there is a similar construct for the 5-connected 5-regular planar graphs. (Maybe I don't need to generate all of them like the title of this post.)

I noted the number of 5-connected 5-regular planar graphs with at most 36 vertices in the following paper.

• Hasheminezhad M, McKay B, Reeves T. Recursive generation of simple planar 5-regular graphs and pentangulations[J]. 2011.

Enough such graphs to convince me there are an unlimited number of such graphs. And when $n$ is large enough, for every $n$ there is a graph that I want.

My question was partly inspired by the question linked below.

• There is a 3-connected 5-regular simple $n$-vertex planar graph iff $n$ satisfies....?

I see a wonderful construction of Adam P. Goucher, which guarantees that 3-connected 5-regular planar graphs are infinitely numerous. I wonder if there is also such a construct for the 5-connected 5-regular planar graphs. (Maybe I don't need to generate all of them like the title of this post.)

I noted the number of 5-connected 5-regular planar graphs with at most 36 vertices in the following paper.

• Hasheminezhad M, McKay B, Reeves T. Recursive generation of simple planar 5-regular graphs and pentangulations[J]. 2011.

Enough such graphs to convince me there are an unlimited number of such graphs.

My question was partly inspired by the question linked below.

• There is a 3-connected 5-regular simple $n$-vertex planar graph iff $n$ satisfies....?

I see a wonderful construction of Adam P. Goucher, which guarantees that 3-connected 5-regular planar graphs are infinitely numerous. I wonder if there is also such a construct for the 5-connected 5-regular planar graphs. (Maybe I don't need to generate all of them like the title of this post.)

I noted the number of 5-connected 5-regular planar graphs with at most 36 vertices in the following paper.

• Hasheminezhad M, McKay B, Reeves T. Recursive generation of simple planar 5-regular graphs and pentangulations[J]. 2011.

Enough such graphs to convince me there are an unlimited number of such graphs. And when $n$ is large enough, for every $n$ there is a graph that I want.

My question was partly inspired by the question linked below.

• There is a 3-connected 5-regular simple $n$-vertex planar graph iff $n$ satisfies....?

I see the wonderful construction of Adam P. Goucher, which guarantees that 3-connected 5-regular planar graphs are infinitely numerous. I wonder if there is also such a construct for the 5-connected 5-regular planar graphs. (Maybe I don't need to generate all of them like the title of this post.)

I noted the number of 5-connected 5-regular planar graphs with at most 36 vertices in the following paper.

• Hasheminezhad M, McKay B, Reeves T. Recursive generation of simple planar 5-regular graphs and pentangulations[J]. 2011.

Enough such graphs to convince me there are an unlimited number of such graphs.

My question was partly inspired by the question linked below.

• There is a 3-connected 5-regular simple $n$-vertex planar graph iff $n$ satisfies....?

I see a wonderful construction of Adam P. Goucher, which guarantees that 3-connected 5-regular planar graphs are infinitely numerous. I wonder if there is also such a construct for the 5-connected 5-regular planar graphs. (Maybe I don't need to generate all of them like the title of this post.)

I noted the number of 5-connected 5-regular planar graphs with at most 36 vertices in the following paper.

• Hasheminezhad M, McKay B, Reeves T. Recursive generation of simple planar 5-regular graphs and pentangulations[J]. 2011.

Enough such graphs to convince me there are an unlimited number of such graphs.