Response to the Referee

We would like to thank the referee for careful reading of the manuscript and for very useful remarks.
We took into consideration all of them. There are a few points that need to be explained.

1. Page 2 - Remark 2. We removed the incomplete definition of Wythoffian operations. Since we only
deal with the medial, there is no need for more general definition. Such a definition would need too 
much space and would distract the reader. The medial itself is correctly defined.

2. Page 18 - Remark 2. We rewrote the last paragraph to explain the notion of the self-Petrie symmetry type 
graph. 

3. Other remarks made by the referee gave direct suggestions and we followed all of them.

4. We expanded the last paragraph of the conclusion in order to point out several possible applications
and generalizations of symmetry type graphs. We also added the following references supporting our claims.

[3] cited in p. 30
[6] cited in p. 7
[13] cited in p. 30
[21] cited in p.30
[26] cited in p.30
[31] cited in p.30