G4.1 Regular tessellation is formed by identical regular $m$-polygons for some fixed $m$. Find the sum of all possible values of $m$.
Each interior angle $=\frac{180^{\circ}(m-2)}{m}(\angle \mathrm{s}$ sum of polygon $)$
Suppose $n m$-polygons tessellate the space.
$$
\begin{array}{l}
\frac{180^{\circ}(m-2)}{m} \cdot n=360^{\circ}(\angle \mathrm{s} \text { at a point }) \\
n(m-2)=2 m \\
n(m-2)-2 m+4=4 \\
(n-2)(m-2)=4 \\
m-2=1,2 \text { or } 4 \\
m=3,4 \text { or } 6
\end{array}
$$

Sum of all possible $m=3+4+6=13$