A note on nearly Platonic graphs with connectivity one

2-nearly Platonic graphs are unique

“…The following result is stated in [1], and a detailed proof is given in [4]. [4]). There are no endblocks of any admissible type.…”

“…We start with some easy observations regarding the graphs of types (3, 3), (3,4), and (4, 3). Observation 5.1.…”

“…Keith, Froncek, and Kreher [5,6] and Froncek and Qiu [4] proved recently that there are no 1-nearly Platonic graphs.…”

On families of 2-nearly Platonic graphs

“…Keith, Froncek, and Kreher [15,16] and Froncek, Khorsandi, Musawi, and Qiu [6] proved recently that there are no 1-nearly Platonic graphs. Deza, Dutour Sikirič, and Shtogrin [4] classified for each admissible pair (k|d) all possible sizes of the exceptional faces of balanced 3-nearly Platonic graphs and sketched a proof of the completeness of the list.…”