Regular Maps on C³

There is no regular map on the non-orientable genus-3 surface^C95.

The table below lists the Schläfli symbols, and numbers of vertices, faces and edges, that such regular maps would have if they existed.

Schläfli symbol	V+F-E=Eu	link to page
{7,3}	14+6-21=-1
{3,7}	6+14-21=-1
{5,4}	5+4-10=-1
{4,5}	4+5-10=-1
{8,3}	8+3+12=-1
{3,8}	3+8-12=-1
{5,5}	2+2-5=-1
{6,4}	3+2-6=-1
{4,6}	2+3-6=-1
{9,3}	6+2-9=-1
{3,9}	2+6-9=-1
{6,6}	1+1-3=-1
{12,3}	4+1-6=-1
{3,12}	1+4-6=-1
{8,4}	2+1-4=-1
{4,8}	1+2-4=-1