Fundamental Polygon

Examples

• sphere: $A\; A^\{-1\}$
• projective plane: $A\; A$
• Klein bottle: $A\; B\; A^\{-1\}\; B$ or $A\; A\; B\; B$
• torus: $A\; B\; A^\{-1\}\; B^\{-1\}$

Standard fundamental polygons

$A\_1\; B\_1\; A\_1^\{-1\}\; B\_1^\{-1\}A\_2\; B\_2\; A\_2^\{-1\}\; B\_2^\{-1\}\backslash cdots\; A\_n\; B\_n\; A\_n^\{-1\}\; B\_n^\{-1\}$

$A\_1\; A\_1\; A\_2\; A\_2\; \backslash cdots\; A\_n\; A\_n$

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