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Find values of p for which the faces of a planar p-regular graph are all triangles.

The faces of a planar p-regular graph are all triangles (that is each face has degree three). Determine, with proof, the values of p for which this is possible. (Remember a p-regular graph has all vertices of degree p).

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Values of p for which the faces of a planar p-regular graph are all triangles are found. The solution is detailed and well presented. The solution received a rating of "5" from the student who posted the question.

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