Abstract:
The paper discusses planar diagrams (called charts by S. Kamada) for
embedded (in $\Re^{4}$) or mapped in general position (in $\Re^{3}$) surfaces and shows that the diagrams are very suitable for dealing with such surfaces and for easy construction of surface mappings with specific properties.
A series of examples is constructed, including an example of a sphere immersion with two triple points and a unique double line.
Key words and phrases:surface-knot, surface-link, diagram, planar, chart, surface, embedded surface, immersed surface, Boy surface, double line, fold line, triple point, branch point, Whitney's umbrella, cusp.