In theses [these notes](https://www.dpmms.cam.ac.uk/~hjrw2/Notes/cubenotes.pdf), Example 5.6, it is said that there is a "symmetric tiling of a genus 2 surface by 8 right-angled hyperbolic pentagons".


Question 1: What does this tiling look like?


Question 2: Is it always possible to tile a genus $n$ surface by $f$ regular $n$-gons with interior angle $\pi/v$ (so that $v$ faces meet at every vertex) as long as the restriction given by the Euler characteristic 
$$\chi=2-2n= f-nf/2+nf/v$$
is satisfied?
Answering [this question](https://mathoverflow.net/questions/198040/regular-tiling-of-a-surface-of-genus-2-by-heptagons?r=searchresults), Igor Rivin says yes, but it seems his argument only shows that regular hyperbolic $n$-gons of interior angle smaller than the interior angle of a euclidean regular $n$-gon exist.



Tiling of genus 2 surface by 8 pentagons
A picture answering Question 1 is here: <https://mathoverflow.net/a/331408/1345>


Question 2 is a duplicate of [regular tiling of a surface of genus 2 by heptagons](https://mathoverflow.net/questions/198040/regular-tiling-of-a-surface-of-genus-2-by-heptagons), although as you point out the accepted answer there is unsatisfactory. I've given a link there answering this question. 


