Each face shares all its vertices with itself. Some readers may consider
that this invalidates it as a regular map.
This genus-3 regular map, shown to the right, has two octagonal faces, each meeting four times at each of its two vertices. It has eight edges, and a Euler characteristic of -4.
Its Petrie polygons have two edges, and its holes have four edges.
It is self-dual. It is a double cover of S2:{8,8}. Its Petrie dual is the 8-hosohedron. It can be cantellated to produce S3:{8,4}.
Its rotational symmetry group is C8×C2.
Each face shares all its vertices with itself. Some readers may consider
that this invalidates it as a regular map.
Each face is antipodal to the other; each vertex is antipodal to the other; the eight edges form a single antipodal set. Rotating one edge about its centre causes every other edge to remain where it is and rotate about its centre: this is the central involution of its rotational symmetry group.
Other regular maps on the genus-3 oriented surface.
Index to other pages on regular maps.
Some pages on groups
Copyright N.S.Wedd 2009