C5:{10,4}

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Statistics

genus ^c	5, non-orientable
Schläfli formula ^c	{10,4}
V / F / E ^c	5 / 2 / 10
notes
vertex, face multiplicity ^c	1, 10
Petrie polygons holes	5, each with 4 edges 2 double, each with 10 edges
antipodal sets	5 of ( v, p1 ), 1 of ( 2f ), 1 of ( 2h )
rotational symmetry group	D10, with 10 elements
full symmetry group	Frob(20), with 20 elements

Relations to other Regular Maps

Its dual is C5:{4,10}.

Its Petrie dual is {4,4}_(2,1).

It can be 2-fold covered to give S4:{10,4}a.

Other regular maps in the same manifold.

Underlying Graph

If we ignore its faces and regard it as a graph, it is isomorphic to K₅.

Comments

We see that this is not a regular map if we arbitrarily label the vertices 0,1,2,3,4 and then follow the perimeter of a face. The vertices occur in the order 0410213243, so only five of the ten rotations of a face are symmetry operations.

Other Regular Maps

General Index