basic question on triangular maps in graph theory

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While doing the book "Probem Solving Strategies by Arthur Engel" I found this question:

"Can you draw a triangular map inside a pentagon, so that each vertex has an even degree?"

I know what degree of a vertex means, however I am not understanding what a triangular map means here? Also how do I solve this problem?

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2 Answers

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You can think of triangular map as of planar graph with all polygons that appear being topologically triangles (i.e. having 3 vertices and 3 edges).

This planar graph is not a triangular map because the face in the middle is quadrilateral. However, if you add diagonal to it, it becomes a triangular map.

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A triangular map is a special case of a Regular map : (graph_theory)

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