The Genus-2 Regular Map {3,8}

This regular map has six 8-valent vertices, 16 triangular faces, and 24 edges.

Its rotational symmetry group is GL(2,3).

Its dual is {8,3}. Its double cover is S³:{3,8}.

Its Petrie polygons are dodecagons, its holes are octagons, its 2nd-order Petrie polygons are octagons, its 3rd-order holes are hexagons, its 4th-order Petrie polygons are dodecagons, and its 4th-order holes are digons.

Its faces form antipodal pairs, as do its vertices, as do its edges.

It can be constructed by taking S²:{4,6} as shown in the first diagram to the left, and superposing the second diagram to the left (whose faces are four triangles and one dodecagonal ring-face) so as to obtain S2{3,8} as shown in the last diagram.